THE DOUBLE ANGLE FORMULA
|
|
|
- Cassandra O’Neal’
- 5 years ago
- Views:
Transcription
1 05 HAWAII UNIVERSITY INTERNATIONAL CONERENCES S.T.E.A.. & EDUCATION JUNE 3-5, 05 ALA OANA HOTEL, HONOLULU, HAWAII S.T.E.A. & EDUCATION PUBLICATION: ISSN (CD-RO ISSN (ONLINE THE DOUBLE ANGLE ORULA O THE ULATU NUBERS ULATU, LEA & ET AL SAVANNAH STATE UNIVERSITY, GEORGIA DEPARTENT O ATHEATICS
2 The Double Agle ormula of the ulatu Numbers ulatu Lemma, Joatha Lambright ad Ermi Asfaw College of Sciece ad Techology Savaah State Uiversity Savaah, GA 3404, U.S.A. Hawaii Uiversity Iteratioal Coferece Abstract: The ulatu umbers were itroduced i []. The umbers are sequeces of umbers of the form: 4,, 5,6,,7,8,45... The umbers have woderful ad amazig properties ad patters. I mathematical terms, the sequece of the ulatu umbers is defied by the followig recurrece relatio: : 4 if 0; if ; if. The double Agel ormulas for iboacci ad Lucas umbers are give by the followig formulas respectively. ( L ad ( L 5 L Sice both the iboacci ad Lucas umbers have double agle ormulas, It is atural to ask if such formula exist for ulatu Numbers. The aswer is affirmative ad produces the followig papers. 000 athematical Subject Classificatio: Key Words: ulatu umbers, ulatu sequeces, iboacci umbers, Lucas umbers, iboacci sequeces, ad Lucas sequeces.. Itroductio ad Backgroud. As give i [], the ulatu umbers are a sequece of umbers recetly itroduced by ulatu Lemma, Professor of athematics at Savaah State Uiversity, Savaah, Georgia, USA. The ulatu sequece has wealthy mathematical properties ad patters like the two celebrity sequeces of iboacci ad Lucas.
3 I this paper, more iterestig relatioships of the ulatu umbers to the iboacci ad Lucas umbers will be preseted. Here are the irst ulatu, iboacci, ad Lucas umbers for quick referece. Table ulatu(, iboacci( ad Lucas(L Numbers ( Tables & : : : L : Table : : L : Remark :Throughout this paper,, ad L stad for ulatu umbers, iboacci umbers, ad Lucas umber respectively. The followig well-kow idetities of ulatu umbers, iboacci umbers, ad Lucas umbers are required i this paper ad hereby listed for quick referece. ( L ( (3 L (4 L
4 (5 L L (6 L L L (7 k k k 5 (8 5 L 4 m LL (9 L m 5 m (0 k k k The ai Results. We will state the followig theorem proved i [] as propositio ad use it. Propositio. = Theorem : The followig are equivalet. ( ( (3 L + (4 +4 (5 4-3 Proof: We will show that ( ( (3 (4 (5 ( (i ( ( follows by Propositio. (ii ( (3 follows as show: = = = = +L (iii(3 (4 follows as show: L + = + + = = +4 (iv (4 (5 follows as show: +4 = + 4( -
5 = 4-3 (v (5 ( follows as show: 4-3 = 4-3( - = +3 = = + ( = = = by Propositio ad hece (5 (. Thus the theorem is proved. Theorem : L = ( + - Proof: L = ( + = = - ( + + ( + ( = - L + + ( + = - L + + = - ( + L + = ( + - L = ( + - Hece the theorem is proved. Theorem Proof : L ( 4 ( = L +4 ( + = = Hece, the theorem is proved. +8 Lemma. = + Proof: Applyig (7 above, we have Lemma. = 5 Proof: usig (0 above, we have = 5 0 = 5. Theorem 4. The followig are equivalet. = = +
6 L L 4 L 5 - L 6. Proof (((3 (4 follows by Theorem. We will suffice to show that (4(5(6 ( (i (4(5. Note that Usig (9 above ad lemma, we have L + 5 L + 9 L 4 + =. (ii (5(6. We show this usig Theorem 3 ad Lemma. Note that 9 L 4 5 L L = = = + = L +4 ( = = ( ( = ( 4 ( + 5 -( + = L L (iii (6(. We show this usig Theorem 3 ad Lemma. Note that L L = L - L + 5 -( = L = L -( +4 = L -( ( = = = L = L + ( 5 (
7 = +. = = Hece, (6( ad the theorem is proved. Corollary : L + 4 Proof: The corollary easily follows by Theorem 4, usig (8 above. Refereces:. ulatu Lemma, The ulatu Numbers, Advaces ad Applicatios i athematical Scieces, Volume 0, issue 4,august 0, page Burto, D.., Elemetary umber theory. New York City, New York: cgraw-hill. 998.
ON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS
Joural of Algebra, Number Theory: Advaces ad Applicatios Volume, Number, 00, Pages 7-89 ON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS OLCAY KARAATLI ad REFİK KESKİN Departmet
SOME TRIBONACCI IDENTITIES
Mathematics Today Vol.7(Dec-011) 1-9 ISSN 0976-38 Abstract: SOME TRIBONACCI IDENTITIES Shah Devbhadra V. Sir P.T.Sarvajaik College of Sciece, Athwalies, Surat 395001. e-mail : drdvshah@yahoo.com The sequece
On the Jacobsthal-Lucas Numbers by Matrix Method 1
It J Cotemp Math Scieces, Vol 3, 2008, o 33, 1629-1633 O the Jacobsthal-Lucas Numbers by Matrix Method 1 Fikri Köke ad Durmuş Bozkurt Selçuk Uiversity, Faculty of Art ad Sciece Departmet of Mathematics,
Observations on Derived K-Fibonacci and Derived K- Lucas Sequences
ISSN(Olie): 9-875 ISSN (Prit): 7-670 Iteratioal Joural of Iovative Research i Sciece Egieerig ad Techology (A ISO 97: 007 Certified Orgaizatio) Vol. 5 Issue 8 August 06 Observatios o Derived K-iboacci
TRACES OF HADAMARD AND KRONECKER PRODUCTS OF MATRICES. 1. Introduction
Math Appl 6 2017, 143 150 DOI: 1013164/ma201709 TRACES OF HADAMARD AND KRONECKER PRODUCTS OF MATRICES PANKAJ KUMAR DAS ad LALIT K VASHISHT Abstract We preset some iequality/equality for traces of Hadamard
On the Fibonacci-like Sequences of Higher Order
Article Iteratioal Joural of oder atheatical Scieces, 05, 3(): 5-59 Iteratioal Joural of oder atheatical Scieces Joural hoepage: wwwoderscietificpressco/jourals/ijsaspx O the Fiboacci-like Sequeces of
A Note On The Exponential Of A Matrix Whose Elements Are All 1
Applied Mathematics E-Notes, 8(208), 92-99 c ISSN 607-250 Available free at mirror sites of http://wwwmaththuedutw/ ame/ A Note O The Expoetial Of A Matrix Whose Elemets Are All Reza Farhadia Received
S. S. Dragomir and Y. J. Cho. I. Introduction In 1956, J. Aczél has proved the following interesting inequality ([2, p. 57], [3, p.
![S. S. Dragomir and Y. J. Cho. I. Introduction In 1956, J. Aczél has proved the following interesting inequality ([2, p. 57], [3, p.](/thumbs/84/90598769.jpg "S. S. Dragomir and Y. J. Cho. I. Introduction In 1956, J. Aczél has proved the following interesting inequality ([2, p. 57], [3, p.")
ON ACZÉL S INEQUALITY FOR REAL NUMBERS S. S. Dragomir ad Y. J. Cho Abstract. I this ote, we poit out some ew iequalities of Aczel s type for real umbers. I. Itroductio I 1956, J. Aczél has proved the followig
A Study on Some Integer Sequences
It. J. Cotemp. Math. Scieces, Vol. 3, 008, o. 3, 03-09 A Study o Some Iteger Sequeces Serpil Halıcı Sakarya Uiversity, Departmet of Mathematics Esetepe Campus, Sakarya, Turkey shalici@sakarya.edu.tr Abstract.
Applied Mathematics Letters. On the properties of Lucas numbers with binomial coefficients
Applied Mathematics Letters 3 (1 68 7 Cotets lists available at ScieceDirect Applied Mathematics Letters joural homepage: wwwelseviercom/locate/aml O the properties of Lucas umbers with biomial coefficiets
Factors of sums and alternating sums involving binomial coefficients and powers of integers
Factors of sums ad alteratig sums ivolvig biomial coefficiets ad powers of itegers Victor J. W. Guo 1 ad Jiag Zeg 2 1 Departmet of Mathematics East Chia Normal Uiversity Shaghai 200062 People s Republic
On Some Properties of Digital Roots
Advaces i Pure Mathematics, 04, 4, 95-30 Published Olie Jue 04 i SciRes. http://www.scirp.org/joural/apm http://dx.doi.org/0.436/apm.04.46039 O Some Properties of Digital Roots Ilha M. Izmirli Departmet
PAijpam.eu ON TENSOR PRODUCT DECOMPOSITION
Iteratioal Joural of Pure ad Applied Mathematics Volume 103 No 3 2015, 537-545 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://wwwijpameu doi: http://dxdoiorg/1012732/ijpamv103i314
On a class of convergent sequences defined by integrals 1
Geeral Mathematics Vol. 4, No. 2 (26, 43 54 O a class of coverget sequeces defied by itegrals Dori Adrica ad Mihai Piticari Abstract The mai result shows that if g : [, ] R is a cotiuous fuctio such that
On Summability Factors for N, p n k
Advaces i Dyamical Systems ad Applicatios. ISSN 0973-532 Volume Number 2006, pp. 79 89 c Research Idia Publicatios http://www.ripublicatio.com/adsa.htm O Summability Factors for N, p B.E. Rhoades Departmet
Right circulant matrices with ratio of the elements of Fibonacci and geometric sequence
Notes o Number Theory ad Discrete Mathematics Prit ISSN 1310 5132, Olie ISSN 2367 8275 Vol. 22, 2016, No. 3, 79 83 Right circulat matrices with ratio of the elemets of Fiboacci ad geometric sequece Aldous
Matrix representations of Fibonacci-like sequences
NTMSCI 6, No. 4, 03-0 08 03 New Treds i Mathematical Scieces http://dx.doi.org/0.085/tmsci.09.33 Matrix represetatios of Fiboacci-like sequeces Yasemi Tasyurdu Departmet of Mathematics, Faculty of Sciece
GAMALIEL CERDA-MORALES 1. Blanco Viel 596, Valparaíso, Chile. s: /
THE GELIN-CESÀRO IDENTITY IN SOME THIRD-ORDER JACOBSTHAL SEQUENCES arxiv:1810.08863v1 [math.co] 20 Oct 2018 GAMALIEL CERDA-MORALES 1 1 Istituto de Matemáticas Potificia Uiversidad Católica de Valparaíso
Super congruences concerning Bernoulli polynomials. Zhi-Hong Sun
It J Numer Theory 05, o8, 9-404 Super cogrueces cocerig Beroulli polyomials Zhi-Hog Su School of Mathematical Scieces Huaiyi Normal Uiversity Huaia, Jiagsu 00, PR Chia zhihogsu@yahoocom http://wwwhytceduc/xsjl/szh
Xhevat Z. Krasniqi and Naim L. Braha
Acta Uiversitatis Apulesis ISSN: 582-5329 No. 23/200 pp. 99-05 ON L CONVERGENCE OF THE R TH DERIVATIVE OF COSINE SERIES WITH SEMI-CONVEX COEFFICIENTS Xhevat Z. Krasiqi ad Naim L. Braha Abstract. We study
Accepted in Fibonacci Quarterly (2007) Archived in SEQUENCE BALANCING AND COBALANCING NUMBERS
Accepted i Fiboacci Quarterly (007) Archived i http://dspace.itrl.ac.i/dspace SEQUENCE BALANCING AND COBALANCING NUMBERS G. K. Pada Departmet of Mathematics Natioal Istitute of Techology Rourela 769 008
ON THE HADAMARD PRODUCT OF BALANCING Q n B AND BALANCING Q n
TWMS J App Eg Math V5, N, 015, pp 01-07 ON THE HADAMARD PRODUCT OF ALANCING Q AND ALANCING Q MATRIX MATRIX PRASANTA KUMAR RAY 1, SUJATA SWAIN, Abstract I this paper, the matrix Q Q which is the Hadamard
NEW FAST CONVERGENT SEQUENCES OF EULER-MASCHERONI TYPE
UPB Sci Bull, Series A, Vol 79, Iss, 207 ISSN 22-7027 NEW FAST CONVERGENT SEQUENCES OF EULER-MASCHERONI TYPE Gabriel Bercu We itroduce two ew sequeces of Euler-Mascheroi type which have fast covergece
SOME SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS
ARCHIVU ATHEATICU BRNO Tomus 40 2004, 33 40 SOE SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS E. SAVAŞ AND R. SAVAŞ Abstract. I this paper we itroduce a ew cocept of λ-strog covergece with respect to a Orlicz
An analog of the arithmetic triangle obtained by replacing the products by the least common multiples
arxiv:10021383v2 [mathnt] 9 Feb 2010 A aalog of the arithmetic triagle obtaied by replacig the products by the least commo multiples Bair FARHI bairfarhi@gmailcom MSC: 11A05 Keywords: Al-Karaji s triagle;
UNIFORMLY CONVERGENT STOLZ THEOREM FOR SEQUENCES OF FUNCTIONS
Fudametal Joural of Mathematics ad Mathematical Scieces Vol. 7, Issue, 207, Pages 5-58 This paper is available olie at http://www.frdit.com/ Published olie March 2, 207 UNIFORMLY CONVERGENT STOLZ THEOREM
Some identities involving Fibonacci, Lucas polynomials and their applications
Bull. Math. Soc. Sci. Math. Roumaie Tome 55103 No. 1, 2012, 95 103 Some idetities ivolvig Fiboacci, Lucas polyomials ad their applicatios by Wag Tigtig ad Zhag Wepeg Abstract The mai purpose of this paper
International Journal of Mathematical Archive-3(4), 2012, Page: Available online through ISSN
Iteratioal Joural of Mathematical Archive-3(4,, Page: 544-553 Available olie through www.ima.ifo ISSN 9 546 INEQUALITIES CONCERNING THE B-OPERATORS N. A. Rather, S. H. Ahager ad M. A. Shah* P. G. Departmet
Sums Involving Moments of Reciprocals of Binomial Coefficients
1 2 3 47 6 23 11 Joural of Iteger Sequeces, Vol. 14 (2011, Article 11.6.6 Sums Ivolvig Momets of Reciprocals of Biomial Coefficiets Hacèe Belbachir ad Mourad Rahmai Uiversity of Scieces ad Techology Houari
II. Pre- Operator Compact Space. Hanan. K. Moussa (Department of Mathimatics, College of Education, AL-Mustansirya University, Iraq)
IOSR Joural of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 11, Issue 6 Ver. II (Nov. - Dec. 2015), PP 37-42 www.iosrjourals.org Haa. K. Moussa (Departmet of Mathimatics, College
Review Article Incomplete Bivariate Fibonacci and Lucas p-polynomials
Discrete Dyamics i Nature ad Society Volume 2012, Article ID 840345, 11 pages doi:10.1155/2012/840345 Review Article Icomplete Bivariate Fiboacci ad Lucas p-polyomials Dursu Tasci, 1 Mirac Ceti Firegiz,
ON SOME GAUSSIAN PELL AND PELL-LUCAS NUMBERS
Ordu Üiv. Bil. Tek. Derg., Cilt:6, Sayı:1, 016,8-18/Ordu Uiv. J. Sci. Tech., Vol:6, No:1,016,8-18 ON SOME GAUSSIAN PELL AND PELL-LUCAS NUMBERS Serpil Halıcı *1 Sia Öz 1 Pamukkale Ui., Sciece ad Arts Faculty,Dept.
Sequences of Definite Integrals, Factorials and Double Factorials
47 6 Joural of Iteger Sequeces, Vol. 8 (5), Article 5.4.6 Sequeces of Defiite Itegrals, Factorials ad Double Factorials Thierry Daa-Picard Departmet of Applied Mathematics Jerusalem College of Techology
GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES
GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES A STUDY ON THE HYPERBOLA x 9 0 S. Vidhyalakshmi, M.A. Gopala & T. Mahalakshmi*, Professor, Departmet of Mathematics, Shrimati Idira Gadhi College, Trichy-60
Reformulation of Shapiro s inequality
Iteratioal Mathematical Forum, Vol. 7, 2012, o. 43, 2125-2130 Reformulatio of Shapiro s iequality Tafer Tariverdi Departmet of Mathematics, Harra Uiversity Saliurfa, 63300 Turkey ttariverdi@harra.edu.tr
On the Inverse of a Certain Matrix Involving Binomial Coefficients
It. J. Cotemp. Math. Scieces, Vol. 3, 008, o. 3, 5-56 O the Iverse of a Certai Matrix Ivolvig Biomial Coefficiets Yoshiari Iaba Kitakuwada Seior High School Keihokushimoyuge, Ukyo-ku, Kyoto, 60-0534, Japa
The 4-Nicol Numbers Having Five Different Prime Divisors
1 2 3 47 6 23 11 Joural of Iteger Sequeces, Vol. 14 (2011), Article 11.7.2 The 4-Nicol Numbers Havig Five Differet Prime Divisors Qiao-Xiao Ji ad Mi Tag 1 Departmet of Mathematics Ahui Normal Uiversity
arxiv: v1 [math.nt] 5 Jan 2017 IBRAHIM M. ALABDULMOHSIN
![arxiv: v1 [math.nt] 5 Jan 2017 IBRAHIM M. ALABDULMOHSIN](/thumbs/89/98516099.jpg "arxiv: v1 [math.nt] 5 Jan 2017 IBRAHIM M. ALABDULMOHSIN")
FRACTIONAL PARTS AND THEIR RELATIONS TO THE VALUES OF THE RIEMANN ZETA FUNCTION arxiv:70.04883v [math.nt 5 Ja 07 IBRAHIM M. ALABDULMOHSIN Kig Abdullah Uiversity of Sciece ad Techology (KAUST, Computer,
Equations and Inequalities Involving v p (n!)
Equatios ad Iequalities Ivolvig v (!) Mehdi Hassai Deartmet of Mathematics Istitute for Advaced Studies i Basic Scieces Zaja, Ira mhassai@iasbs.ac.ir Abstract I this aer we study v (!), the greatest ower
CSE 1400 Applied Discrete Mathematics Number Theory and Proofs
CSE 1400 Applied Discrete Mathematics Number Theory ad Proofs Departmet of Computer Scieces College of Egieerig Florida Tech Sprig 01 Problems for Number Theory Backgroud Number theory is the brach of
Bijective Proofs of Gould s and Rothe s Identities
ESI The Erwi Schrödiger Iteratioal Boltzmagasse 9 Istitute for Mathematical Physics A-1090 Wie, Austria Bijective Proofs of Gould s ad Rothe s Idetities Victor J. W. Guo Viea, Preprit ESI 2072 (2008 November
The Borel-Cantelli Lemma and its Applications
The Borel-Catelli Lemma ad its Applicatios Ala M. Falleur Departmet of Mathematics ad Statistics The Uiversity of New Mexico Albuquerque, New Mexico, USA Dig Li Departmet of Electrical ad Computer Egieerig
MAJORIZATION PROBLEMS FOR SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING
Iteratioal Joural of Civil Egieerig ad Techology (IJCIET) Volume 9, Issue, November 08, pp. 97 0, Article ID: IJCIET_09 6 Available olie at http://www.ia aeme.com/ijciet/issues.asp?jtypeijciet&vtype 9&IType
Some Trigonometric Identities Involving Fibonacci and Lucas Numbers
1 2 3 47 6 23 11 Joural of Iteger Sequeces, Vol. 12 (2009), Article 09.8.4 Some Trigoometric Idetities Ivolvig Fiboacci ad Lucas Numbers Kh. Bibak ad M. H. Shirdareh Haghighi Departmet of Mathematics Shiraz
On the Number of 1-factors of Bipartite Graphs
Math Sci Lett 2 No 3 181-187 (2013) 181 Mathematical Scieces Letters A Iteratioal Joural http://dxdoiorg/1012785/msl/020306 O the Number of 1-factors of Bipartite Graphs Mehmet Akbulak 1 ad Ahmet Öteleş
Dominating Sets and Domination Polynomials of Square Of Cycles
IOSR Joural of Mathematics IOSR-JM) ISSN: 78-78. Volume 3, Issue 4 Sep-Oct. 01), PP 04-14 www.iosrjourals.org Domiatig Sets ad Domiatio Polyomials of Square Of Cycles A. Vijaya 1, K. Lal Gipso 1 Assistat
Benaissa Bernoussi Université Abdelmalek Essaadi, ENSAT de Tanger, B.P. 416, Tanger, Morocco
EXTENDING THE BERNOULLI-EULER METHOD FOR FINDING ZEROS OF HOLOMORPHIC FUNCTIONS Beaissa Beroussi Uiversité Abdelmalek Essaadi, ENSAT de Tager, B.P. 416, Tager, Morocco e-mail: Beaissa@fstt.ac.ma Mustapha
Pell and Lucas primes
Notes o Number Theory ad Discrete Mathematics ISSN 30 532 Vol. 2, 205, No. 3, 64 69 Pell ad Lucas primes J. V. Leyedekkers ad A. G. Shao 2 Faculty of Sciece, The Uiversity of Sydey NSW 2006, Australia
#A51 INTEGERS 14 (2014) MULTI-POLY-BERNOULLI-STAR NUMBERS AND FINITE MULTIPLE ZETA-STAR VALUES
#A5 INTEGERS 4 (24) MULTI-POLY-BERNOULLI-STAR NUMBERS AND FINITE MULTIPLE ZETA-STAR VALUES Kohtaro Imatomi Graduate School of Mathematics, Kyushu Uiversity, Nishi-ku, Fukuoka, Japa k-imatomi@math.kyushu-u.ac.p
Generalized Fibonacci-Like Sequence and. Fibonacci Sequence
It. J. Cotep. Math. Scieces, Vol., 04, o., - 4 HIKARI Ltd, www.-hiari.co http://dx.doi.org/0.88/ijcs.04.48 Geeralized Fiboacci-Lie Sequece ad Fiboacci Sequece Sajay Hare epartet of Matheatics Govt. Holar
MONOTONICITY OF SEQUENCES INVOLVING GEOMETRIC MEANS OF POSITIVE SEQUENCES WITH LOGARITHMICAL CONVEXITY
MONOTONICITY OF SEQUENCES INVOLVING GEOMETRIC MEANS OF POSITIVE SEQUENCES WITH LOGARITHMICAL CONVEXITY FENG QI AND BAI-NI GUO Abstract. Let f be a positive fuctio such that x [ f(x + )/f(x) ] is icreasig
The Asymptotic Expansions of Certain Sums Involving Inverse of Binomial Coefficient 1
Iteratioal Mathematical Forum, 5, 2, o. 6, 76-768 The Asymtotic Easios of Certai Sums Ivolvig Iverse of Biomial Coefficiet Ji-Hua Yag Deartmet of Mathematics Zhoukou Normal Uiversity, Zhoukou 466, P.R.
Reciprocal Series of K Fibonacci Numbers with Subscripts in Linear Form
IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578 p-issn: 39-765X Volume Issue 6 Ver IV (Nov - Dec06) PP 39-43 wwwiosrjouralsorg Reciprocal Series of K iboacci Numbers with Subscripts i iear orm Sergio
On Generalized Fibonacci Numbers
Applied Mathematical Scieces, Vol. 9, 215, o. 73, 3611-3622 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/ams.215.5299 O Geeralized Fiboacci Numbers Jerico B. Bacai ad Julius Fergy T. Rabago Departmet
Commutativity in Permutation Groups
Commutativity i Permutatio Groups Richard Wito, PhD Abstract I the group Sym(S) of permutatios o a oempty set S, fixed poits ad trasiet poits are defied Prelimiary results o fixed ad trasiet poits are
Pellian sequence relationships among π, e, 2
otes o umber Theory ad Discrete Mathematics Vol. 8, 0, o., 58 6 Pellia sequece relatioships amog π, e, J. V. Leyedekkers ad A. G. Shao Faculty of Sciece, The Uiversity of Sydey Sydey, SW 006, Australia
ON THE BINARY QUADRATIC DIOPHANTINE EQUATION
Iteratioal Joural of Scietific Egieerig ad Applied Sciece (IJSEAS) - Volume-, Issue-4, Jue 0 ISSN: 9-470 ON THE BINARY QUADRATIC DIOPHANTINE EQUATION - 6 0 M.A.Gopala * V.Geetha, D.Priaka. Professor, Departmet
k-generalized FIBONACCI NUMBERS CLOSE TO THE FORM 2 a + 3 b + 5 c 1. Introduction
Acta Math. Uiv. Comeiaae Vol. LXXXVI, 2 (2017), pp. 279 286 279 k-generalized FIBONACCI NUMBERS CLOSE TO THE FORM 2 a + 3 b + 5 c N. IRMAK ad M. ALP Abstract. The k-geeralized Fiboacci sequece { F (k)
ANTI-LECTURE HALL COMPOSITIONS AND ANDREWS GENERALIZATION OF THE WATSON-WHIPPLE TRANSFORMATION
ANTI-LECTURE HALL COMPOSITIONS AND ANDREWS GENERALIZATION OF THE WATSON-WHIPPLE TRANSFORMATION SYLVIE CORTEEL, JEREMY LOVEJOY AND CARLA SAVAGE Abstract. For fixed ad k, we fid a three-variable geeratig
Weakly Connected Closed Geodetic Numbers of Graphs
Iteratioal Joural of Mathematical Aalysis Vol 10, 016, o 6, 57-70 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/101988/ijma01651193 Weakly Coected Closed Geodetic Numbers of Graphs Rachel M Pataga 1, Imelda
Fixed Point Theorems for Expansive Mappings in G-metric Spaces
Turkish Joural of Aalysis ad Number Theory, 7, Vol. 5, No., 57-6 Available olie at http://pubs.sciepub.com/tjat/5//3 Sciece ad Educatio Publishig DOI:.69/tjat-5--3 Fixed Poit Theorems for Expasive Mappigs
A generalization of Fibonacci and Lucas matrices
Discrete Applied Mathematics 56 28) 266 269 wwwelseviercom/locate/dam A geeralizatio of Fioacci ad Lucas matrices Predrag Staimirović, Jovaa Nikolov, Iva Staimirović Uiversity of Niš, Departmet of Mathematics,
Continued Fractions and Pell s Equation
Max Lah Joatha Spiegel May, 06 Abstract Cotiued fractios provide a useful, ad arguably more atural, way to uderstad ad represet real umbers as a alterative to decimal expasios I this paper, we eumerate
You may work in pairs or purely individually for this assignment.
CS 04 Problem Solvig i Computer Sciece OOC Assigmet 6: Recurreces You may work i pairs or purely idividually for this assigmet. Prepare your aswers to the followig questios i a plai ASCII text file or
COMMON FIXED POINT THEOREMS VIA w-distance
Bulleti of Mathematical Aalysis ad Applicatios ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 3, Pages 182-189 COMMON FIXED POINT THEOREMS VIA w-distance (COMMUNICATED BY DENNY H. LEUNG) SUSHANTA
1. Introduction. g(x) = a 2 + a k cos kx (1.1) g(x) = lim. S n (x).
Georgia Mathematical Joural Volume 11 (2004, Number 1, 99 104 INTEGRABILITY AND L 1 -CONVERGENCE OF MODIFIED SINE SUMS KULWINDER KAUR, S. S. BHATIA, AND BABU RAM Abstract. New modified sie sums are itroduced
SOME TRIGONOMETRIC IDENTITIES RELATED TO POWERS OF COSINE AND SINE FUNCTIONS
Folia Mathematica Vol. 5, No., pp. 4 6 Acta Uiversitatis Lodziesis c 008 for Uiversity of Lódź Press SOME TRIGONOMETRIC IDENTITIES RELATED TO POWERS OF COSINE AND SINE FUNCTIONS ROMAN WITU LA, DAMIAN S
Local Approximation Properties for certain King type Operators
Filomat 27:1 (2013, 173 181 DOI 102298/FIL1301173O Published by Faculty of Scieces ad athematics, Uiversity of Niš, Serbia Available at: http://wwwpmfiacrs/filomat Local Approimatio Properties for certai
International Journal of Multidisciplinary Research and Development. M.A. Gopalan, A. Kavitha, G. Thamaraiselvi
Volume:, Issue: 6, -7 Jue 015.allsubjectjoural.com e-issn: 49-418 p-issn: 49-5979 Impact Factor:.76 M.A. Gopala Professor, Departmet of Idira Gadhi College, Trichy-6000, Tamiladu, Idia. A. Kavitha Lecturer,
Yuki Seo. Received May 23, 2010; revised August 15, 2010
Scietiae Mathematicae Japoicae Olie, e-00, 4 45 4 A GENERALIZED PÓLYA-SZEGÖ INEQUALITY FOR THE HADAMARD PRODUCT Yuki Seo Received May 3, 00; revised August 5, 00 Abstract. I this paper, we show a geeralized
Warped, Chirp Z-Transform: Radar Signal Processing
arped, Chirp Z-Trasform: Radar Sigal Processig by Garimella Ramamurthy Report o: IIIT/TR// Cetre for Commuicatios Iteratioal Istitute of Iformatio Techology Hyderabad - 5 3, IDIA Jauary ARPED, CHIRP Z
Some remarks on the paper Some elementary inequalities of G. Bennett
Soe rears o the paper Soe eleetary iequalities of G. Beett Dag Ah Tua ad Luu Quag Bay Vieta Natioal Uiversity - Haoi Uiversity of Sciece Abstract We give soe couterexaples ad soe rears of soe of the corollaries
The Arakawa-Kaneko Zeta Function
The Arakawa-Kaeko Zeta Fuctio Marc-Atoie Coppo ad Berard Cadelpergher Nice Sophia Atipolis Uiversity Laboratoire Jea Alexadre Dieudoé Parc Valrose F-0608 Nice Cedex 2 FRANCE Marc-Atoie.COPPO@uice.fr Berard.CANDELPERGHER@uice.fr
Some integrals related to the Basel problem
November, 6 Some itegrals related to the Basel problem Khristo N Boyadzhiev Departmet of Mathematics ad Statistics, Ohio Norther Uiversity, Ada, OH 458, USA k-boyadzhiev@ouedu Abstract We evaluate several
The value of Banach limits on a certain sequence of all rational numbers in the interval (0,1) Bao Qi Feng
The value of Baach limits o a certai sequece of all ratioal umbers i the iterval 0, Bao Qi Feg Departmet of Mathematical Scieces, Ket State Uiversity, Tuscarawas, 330 Uiversity Dr. NE, New Philadelphia,
Asymptotic distribution of products of sums of independent random variables
Proc. Idia Acad. Sci. Math. Sci. Vol. 3, No., May 03, pp. 83 9. c Idia Academy of Scieces Asymptotic distributio of products of sums of idepedet radom variables YANLING WANG, SUXIA YAO ad HONGXIA DU ollege
Some Common Fixed Point Theorems in Cone Rectangular Metric Space under T Kannan and T Reich Contractive Conditions
ISSN(Olie): 319-8753 ISSN (Prit): 347-671 Iteratioal Joural of Iovative Research i Sciece, Egieerig ad Techology (A ISO 397: 7 Certified Orgaizatio) Some Commo Fixed Poit Theorems i Coe Rectagular Metric
Linear recurrence sequences and periodicity of multidimensional continued fractions
arxiv:1712.08810v1 [math.nt] 23 Dec 2017 Liear recurrece sequeces ad periodicity of multidimesioal cotiued fractios Nadir Murru Departmet of Mathematics Uiversity of Turi 10123 Turi, Italy E-mail: adir.murru@uito.it
University of Twente The Netherlands
Faculty of Mathematical Scieces t Uiversity of Twete The Netherlads P.O. Box 7 7500 AE Eschede The Netherlads Phoe: +3-53-4893400 Fax: +3-53-48934 Email: memo@math.utwete.l www.math.utwete.l/publicatios
ON MONOTONICITY OF SOME COMBINATORIAL SEQUENCES
Publ. Math. Debrece 8504, o. 3-4, 85 95. ON MONOTONICITY OF SOME COMBINATORIAL SEQUENCES QING-HU HOU*, ZHI-WEI SUN** AND HAOMIN WEN Abstract. We cofirm Su s cojecture that F / F 4 is strictly decreasig
ON SOME INEQUALITIES IN NORMED LINEAR SPACES
ON SOME INEQUALITIES IN NORMED LINEAR SPACES S.S. DRAGOMIR Abstract. Upper ad lower bouds for the orm of a liear combiatio of vectors are give. Applicatios i obtaiig various iequalities for the quatities
Proof of a conjecture of Amdeberhan and Moll on a divisibility property of binomial coefficients
Proof of a cojecture of Amdeberha ad Moll o a divisibility property of biomial coefficiets Qua-Hui Yag School of Mathematics ad Statistics Najig Uiversity of Iformatio Sciece ad Techology Najig, PR Chia
(p, q)-type BETA FUNCTIONS OF SECOND KIND
Adv. Oper. Theory 6, o., 34 46 http://doi.org/.34/aot.69. ISSN: 538-5X electroic http://aot-math.org p, q-type BETA FUNCTIONS OF SECOND KIND ALI ARAL ad VIJAY GUPTA Commuicated by A. Kamisa Abstract. I
Square-Congruence Modulo n
Square-Cogruece Modulo Abstract This paper is a ivestigatio of a equivalece relatio o the itegers that was itroduced as a exercise i our Discrete Math class. Part I - Itro Defiitio Two itegers are Square-Cogruet
FLOOR AND ROOF FUNCTION ANALOGS OF THE BELL NUMBERS. H. W. Gould Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 (2007), #A58 FLOOR AND ROOF FUNCTION ANALOGS OF THE BELL NUMBERS H. W. Gould Departmet of Mathematics, West Virgiia Uiversity, Morgatow, WV
On Bilateral Generating Relation for a Sequence of Functions
It. Joural of Math. Aalysis, Vol. 2, 2008, o. 8, 383-389 O Bilateral Geeratig Relatio for a Sequece of Fuctios A. K. Shukla ad J. C. Prajapati Departmet of Mathematics S.V. Natioal Istitute of Techology,
Tauberian Conditions in Terms of General Control Modulo of Oscillatory Behavior of Integer Order of Sequences
Iteratioal Mathematical Forum, 2, 2007, o. 20, 957-962 Tauberia Coditios i Terms of Geeral Cotrol Modulo of Oscillatory Behavior of Iteger Order of Sequeces İ. Çaak Departmet of Math., Ada Mederes Uiversity,
A note on the p-adic gamma function and q-changhee polynomials
Available olie at wwwisr-publicatioscom/jmcs J Math Computer Sci, 18 (2018, 11 17 Research Article Joural Homepage: wwwtjmcscom - wwwisr-publicatioscom/jmcs A ote o the p-adic gamma fuctio ad q-chaghee
Strong Convergence Theorems According. to a New Iterative Scheme with Errors for. Mapping Nonself I-Asymptotically. Quasi-Nonexpansive Types
It. Joural of Math. Aalysis, Vol. 4, 00, o. 5, 37-45 Strog Covergece Theorems Accordig to a New Iterative Scheme with Errors for Mappig Noself I-Asymptotically Quasi-Noexpasive Types Narogrit Puturog Mathematics
GENERALIZED HARMONIC NUMBER IDENTITIES AND A RELATED MATRIX REPRESENTATION
J Korea Math Soc 44 (2007), No 2, pp 487 498 GENERALIZED HARMONIC NUMBER IDENTITIES AND A RELATED MATRIX REPRESENTATION Gi-Sag Cheo ad Moawwad E A El-Miawy Reprited from the Joural of the Korea Mathematical
ON SOLVING A FORMAL HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION IN THE COMPLEX FIELD
A. Şt. Uiv. Ovidius Costaţa Vol. (), 003, 69 78 ON SOLVING A FORMAL HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION IN THE COMPLEX FIELD Nicolae Popoviciu To Professor Silviu Sburla, at his 60 s aiversary Abstract
arxiv: v3 [math.nt] 24 Dec 2017
![arxiv: v3 [math.nt] 24 Dec 2017](/thumbs/85/92905221.jpg "arxiv: v3 [math.nt] 24 Dec 2017")
DOUGALL S 5 F SUM AND THE WZ-ALGORITHM Abstract. We show how to prove the examples of a paper by Chu ad Zhag usig the WZ-algorithm. arxiv:6.085v [math.nt] Dec 07 Keywords. Geeralized hypergeometric series;
Mi-Hwa Ko and Tae-Sung Kim
J. Korea Math. Soc. 42 2005), No. 5, pp. 949 957 ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY ORTHANT DEPENDENT RANDOM VARIABLES Mi-Hwa Ko ad Tae-Sug Kim Abstract. For weighted sum of a sequece
A NOTE ON PASCAL S MATRIX. Gi-Sang Cheon, Jin-Soo Kim and Haeng-Won Yoon
J Korea Soc Math Educ Ser B: Pure Appl Math 6(1999), o 2 121 127 A NOTE ON PASCAL S MATRIX Gi-Sag Cheo, Ji-Soo Kim ad Haeg-Wo Yoo Abstract We ca get the Pascal s matrix of order by takig the first rows
BIRKHOFF ERGODIC THEOREM
BIRKHOFF ERGODIC THEOREM Abstract. We will give a proof of the poitwise ergodic theorem, which was first proved by Birkhoff. May improvemets have bee made sice Birkhoff s orgial proof. The versio we give
Research Article Approximate Riesz Algebra-Valued Derivations
Abstract ad Applied Aalysis Volume 2012, Article ID 240258, 5 pages doi:10.1155/2012/240258 Research Article Approximate Riesz Algebra-Valued Derivatios Faruk Polat Departmet of Mathematics, Faculty of
Abstract We obtain infinitely many non-zero integer sextuples ( x, y, z, w, p, T )
IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY O the No-Homogeeous Equatio of the Eighth Degree with Six Ukows x 5 -y 5 +(x 3 -y 3 xy = p(z -w T 3 S.Vidhyalakshmi *1, K.Lakshmi,
THE N-POINT FUNCTIONS FOR INTERSECTION NUMBERS ON MODULI SPACES OF CURVES
THE N-POINT FUNTIONS FOR INTERSETION NUMBERS ON MODULI SPAES OF URVES KEFENG LIU AND HAO XU Abstract. We derive from Witte s KdV equatio a simple formula of the -poit fuctios for itersectio umbers o moduli
Equivalent Banach Operator Ideal Norms 1
It. Joural of Math. Aalysis, Vol. 6, 2012, o. 1, 19-27 Equivalet Baach Operator Ideal Norms 1 Musudi Sammy Chuka Uiversity College P.O. Box 109-60400, Keya sammusudi@yahoo.com Shem Aywa Maside Muliro Uiversity
International Research Journal of Engineering and Technology (IRJET) e-issn: ON THE BINARY QUADRATIC DIOPHANTINE EQUATION
Iteratioal Research Joural of Egieerig ad Techolog (IRJET) e-issn: 9-006 Volume: 0 Issue: 04 Jul-0 www.irjet.et p-issn: 9-007 ON THE BINARY QUADRATIC DIOPHANTINE EQUATION - + 8 = 0 S.Vidhalakshmi, M.A.Gopala,