Two Ridiculous Summation Formulae arising from the summation formulae of Salahuddin et al
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1 Two Ridiculous Summation Formulae arising from the summation formulae of Salahuddin et al Intazar Husain 1 and Salahuddin 2 1 Department of Applied Sciences and Humanities, Jamia Millia Islamia, New Delhi, India 2 P.D.M College of Engineering, Bahadurgarh,Haryana, India *** Abstract - In this paper, we have established two 2010 MSC NO: 33C05, 33C20, 33C60 summation formulae with the help of contiguous relation, derived formulae of Salahuddin et al and 1. INTRODUCTION AND RESULTS REQUIRED using Mathematica. Key Words: Contiguous relation, Summation formulae,prudnikov et al. Abstract In this paper, we have established two summation formulae with the help of contiguous relation, derived formulae of Salahuddin et al and using Mathematica. Key Words : Contiguous relation, Summation formulae,prudnikov et al. Special functions and their uses are now spectacular in their scope. Moreover, their rapid growth in pure Mathematics and its applications to the traditional fields of Physics, Engineering and Statistics but in new fields of applications like scientific computing, Optimization, Biology, Environmental Science and Economics,Management etc. they are emerging. Summation formulae for hypergeometric function has an important role in applied mathematics. Prudnikov et al[2,p.414] derived the following seven summation formulae (1) (2) (3) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 110
![558] (8) Salahuddin et al[3,4,5] derived the following](/docs-images/82/85697138/images/2-1.jpg "thirteen summation formulae 2016, IRJET Impact Factor")
2 (4) (5) (6) (7) The contiguous relation is defined as Abramowitz et al[1,p.558] (8) Salahuddin et al[3,4,5] derived the following thirteen summation formulae 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 111
3 (9) (10) (11) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 112
4 (12) (13) (14) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 113
5 (15) (16) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 114
6 (17) (18) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 115
7 (19) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 116
8 (20) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 117
9 2. MAIN SUMMATION FORMULAE (21) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 118
10 (22) 2016, IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 119
11 (23) ) 3. DERIVATION OF THE MAIN FORMULAE Involving the contiguous relation (8) and the formula of Salahuddin et al(21), one can established the result(22) and on the same way result(23) can be established. References 1. Abramowitz, Milton., A and Stegun, Irene ; Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Prudnikov, A.P., Brychkov, Yu. A. and Marichev, O.I.; Integral and Series Vol 3: More Special Functions,Nauka, Moscow, Salahuddin, Khola, R. K.;New hypergeometric summation formulae arising from the summation formulae of Prudnikov, South Asian Journal of Mathematics,4(2014), Salahuddin, Khola, R. K.;Certain new Hypergeometric Summation formulae arising from the summation formulae of Salahuddin et al, Sohag Journal of Mathematics,3(2016), Salahuddin, Pandit,U. K. and Chaudhary, M. P.;Two Incredible Summation Formula Involving Computational Technique, Global Journal of Science Frontier Research: F,15(2015), , IRJET Impact Factor value: 4.45 ISO 9001:2008 Certified Journal Page 120
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