International Journal of Pure and Applied Sciences and Technology

I. J. Pur Al. S. Thol.. 4-6 Iraoal Joural o Pur ad Ald S ad Tholog ISSN 9-67 Avalabl ol a www.joaaa. Rarh Par Blaral Lala-Mll Igral Traorm ad Alao S.M. Kharar * R.M. P ad J. N. Saluk 3 Darm o Egrg Mahma Maharahra Aadm o Egrg Alad- 45Pu Ida Darm o Mahma A.S.&H. R.G.I.T. Vrova AdhrW Mumba-53 Ida 3 Darm o Mahma Norh Maharahra Uvr Jalgao Maharahra-Ida * Corrodg auhor -mal: mkharar7@gmal.om Rvd: 7-- ; Ad: 9-- Abra: I h ar w du B-laral Lala Mll Igral Traorm hqu or olvg boudar ad al valu rob. Th Traorm udd h rgo - o. W vga h ror ad horm lk vro horm ovoluo horm Parval horm ad om ror b ug Ramauja ormula. To llura h advaag ad u o h raormao Cauh dral quao hav b olvd. Th work gv u a gh o udrad how h raorm a b ud or dg h rlao wh ohr gral raorm. W hav alo udd grahal rrao o B-laral Lala Mll Igral Traorm ug Malab. Kword: Lala Traorm F Mll Traorm Igral Traorm Doubl B Laral Lala Traorm Covoluo ad Parval horm.

I. J. Pur Al. S. Thol. 4-6 5. Iroduo Th Doubl B Laral Lala Traorm ud o d h B -Laral Lala - Mll Igral Traorm h rag - o.w hav drvd h dr ror lk Lar Pror Salg Pror Powr Pror. Ivro Thorm Covoluo Thorm Parval Thorm Fr ad Sod Shg horm ar alo obad b ug Ramauja ormula. W ud h ordr drvav h oluo o h Cauh Lar dral quao ug h B- Laral Lala - Mll Igral raorm h rag - o ad h oluo grahall rrd b ug Malab.. Prar Rul Th Doubl B Laral Lala Igral Traorm o L L dd whvr h doubl gral ad >o > uu d - d d -d - h ad h h L L dd rovdd h doubl gral ad >o > Th h B -Laral Lala Mll Igral Traorm BLLMIT h rag - o. I dod b h dd 3 3. Rul ad Duo 3.. Pror 3..: Lar Pror Th BLLMIT a lar orao horm or h uo z ad g z ad α ar β oa h h BLLMIT - o. 5

I. J. Pur Al. S. Thol. 4-6 6 h dd α βg α β 4 3...: Salg Pror Th alg ror or BLLMIT - o. dd h d q d 3..3: Powr ror Th owr ror or BLLMIT - o. dd h r q / 5 Lm 6 3.. Ma Rul 3..: Ivro Thorm Aum ha z a rgular uo h r R < r r b ral umbr o h -la ad <<ν - whr oa ad R < q q b ral umbr o h -la ad <<ν - whr oa. h h BLLMIT - o. h dd dd 6

I. J. Pur Al. S. Thol. 4-6 7 7 Proo I d L h vr d L ad h Mll Traorm dz z z z M h vr z d z M z. Th BlLMIT - o dd h dd dd dd dd dd d d dd dd dd B aumg ad Th h Ivr o Lala- Mll Igral Traorm.

I. J. Pur Al. S. Thol. 4-6 8 8 I dod b z dd or dd 7 3... Covoluo Thorm Th BlLMIT - o dd h zg- dd g Proo Th BLLMIT - o. dd h g- dd g g dd dd dd g dd dd g g-

I. J. Pur Al. S. Thol. 4-6 9 9 dd g 8 3..3: Paraval Thorm Th BLLMIT - o. dd h zg dd g Proo Th BLLMIT - o. dd h g- dd g g dd dd dd g dd dd g g- dd g 9 3..4: Do U S Fuo:-- I HU wh > wh <

I. J. Pur Al. S. Thol. 4-6 h HU kow a h u uo. bhvd U S Fuo I H-aU-awh >a wh <a h H-aU-a kow a h Hvd U S Fuo 3..5: Fr hg Thorm Th BLLMIT - o. Th dd m Proo Th BLLMIT - o. Th dd a m a m dd a m dd -a m a m -a m 3..6: Sod hg Thorm Th BlLMIT - o

I. J. Pur Al. S. Thol. 4-6 dd Proo Th BILMIT - o dd h - U- dd U ubu -uddu h u- ad h u - U- dd u U u u dd u U u u u- ;- - U- u- ;- 3..7: Thorm Ramauja Formula I r r d r φ φ h dd d d d d dd L--

I. J. Pur Al. S. Thol. 4-6 whr L- d h h Lala Traorm o - w.r..aramr > dod b L{- 3.3. Drvav Thorm: Suo ha z ouou or all ad z ag. or om valu γ η ad m ad ha a drvav z whh w ouou o vr rval h rag o. ad z Th b ug h B Laral Lala Mll Igral Traorm h drvav o z wh > γ ad >η ad z m γ η z or all ad z or om oa 3.3.: BLLMIT o r ordr aral drvav o w. r.. Th BlLMIT - o Th dd z d d d d dd d d B aumg - dd d z - k 3 whr k d 3.3.: BLLMIT o r ordr aral drvav o w.r..

I. J. Pur Al. S. Thol. 4-6 3 z dd dd d d d d d d - dd d - dd B ug DUIS - - k --- -k -k z -k 4 whr k d 3.4: Alao: Th Cauh lar Dral Equao oa varabl. Th BLLMIT o dd dd dd dd 3

I. J. Pur Al. S. Thol. 4-6 4 -k- k - k I h -k k k 5 whr k d Th h rqurd BLLMIT o Cauh Lar Dral Equao. 3.5. Grahal Rrao o BLLMIT o Cauh Lar Dral Equao k whr k d 8 lo o lo or :: -a 6 4...3.4.5 -a Plo o :W odr.. BLLMIT - o o -a ad aramr o -a. 4. Coluo 4

I. J. Pur Al. S. Thol. 4-6 5 W hav obad rg rul o Blaral Lala Mll gral raorm b ug Ramauja ormula. To llura h advaag ad u o h raorm om mora dral quao ha b olvd. W hav alo udd grahal rrao o h oluo ug Malab. Akowldgm Th r auhor hakul ad akowldg h uor rom h rarh roj udd rom h Darm o S ad Tholog R. No. SR/S4/MS:544/8 Govrm o Ida Naoal Board o Hghr Mahma Darm o Aom Erg R. No.NBHM/DAE/R.P./9 Govrm o Ida ad BCUD Uvr o Pu UOP Pu R No.BCUD/4/Egg.9 ad UGC Nw Dlh 47-99 / 9 / WRO. Rr Drk Nalor O a Mll T Igral Traorm Joural o Mahma ad Mha 963. C. Fo Alao o Mll' Traormao o h gral quao 933 3 J. M. Mdz ad J. R.Ngr O h Hakl-Shwarz Traormao o Drbuo Gaa 39 988. 4.Ia N. Sddo Th u o Igral Traorm TMH do 974. 5 C.Fo Alao o Mll Traormao o Igral Equao 3rd Marh 934 495-5. 6 A. H. Zmaa Gralzd Igal Traormao Ir Publao Nw York 968 7 A. Z.Zmaa Th drbuoal Lala ad Mll raormao J. SIAM 4 98. 8 I. S. Rd Th Mll T Doubl Igral Cambrdg Lodo. 9 Sha Drrod ad Faouz Ghorbl Robu ad E Fourr-Mll Traorm Aomao or Gra-Lvl Imag Rorruo ad Coml Ivar Dro Comur Vo ad Imag Udradd 83 57-78. A.E. Gra ad M. Sa A omaro bw Fourr-Mll dror ad Mom bad aur or vara obj rogo ug ural work Par Rog. L. 99 635-643. Rugra Praa Gg Sard Wh Malab Oord Uvr Pr NwYork 3. 5

I. J. Pur Al. S. Thol. 4-6 6 Bru Llld Marg Malab Pr Hall Ur addl Rvr Nw York 3 S. M. Kharar R.M. P ad J. N. Saluk Alao o h Mll gral raorm h rag /a IJMSA Ad. 4 S. M. Kharar R.M. P ad J. N. Saluk Sud O Th Sumudu Mll Igral Traorm ad I Alao I. J. Ma. S. ad Egg. Al. 4IV 37-35. 5 Ja M. Thuh ad Nmvua S. Mhar A alao o doubl Sumudu Traorm Ald Mahmaal S 7 3-39. 6