Global Joual o Scece Fote Reeach atheatc ad Deco Scece Volue Iue Veo Te : Double Bld ee Reewed Iteatoal Reeach Joual ublhe: Global Joual Ic SA Ole ISSN: 49-466 & t ISSN: 975-5896 Soe Itegal etag Bothogoal oloal ad Ceta oduct o Secal Fucto B ooa S NIS et Ida Abtact - The a obect o th ae to obta oe tegal ad ee elato etag to bothogoal oloal Fo H-ucto the geeal cla o oloal ad the H- ucto o eeal cole aable Kewod : Fo H-ucto the geeal cla o oloal ad the H-ucto o cole aable GJSFR-F Clacato : SC : 4K Stctl a e the colace ad egulato o : ooa S Th a eeach/eew ae dtbuted ude the te o the Ceate Coo Attbuto- Nocoecal 3 oted Lcee htt://ceatecooog/lcee/b-c/3/ ettg all o coecal ue dtbuto ad eoducto a edu oded the ogal wo oel cted
Re 7 abhaa TR ad Toa RC Soe tegal ad ee elato o bothogoal oloal uggeted b the Legede oloal Ida J ue al ath 7 98 863-869 Soe Itegal etag Bothogoal oloal ad Ceta oduct o Secal Fucto ooa S Abtact -The a obect o th ae to obta oe tegal ad ee elato etag to bothogoal oloal Fo H-ucto the geeal cla o oloal ad the H-ucto o eeal cole aable Kewod : Fo H-ucto the geeal cla o oloal ad the H-ucto o cole aable I Itoducto Itegal wth Fo H-ucto the geeal cla o oloal ad the H- ucto o cole aable wee tuded b a autho abhaa ad Toa [7 hae ge a bothogoal a o oloal et whee ad V ad V / The geeal ultaable oloal deed b Sataa [ 85 e 7 eeeted the ollowg ae: S [ / [ / [ Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I Autho : NIS et Jau Ratha Ida Global Joual Ic S
L [ ;; whee 3 Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I ae o-eo abta ote tege The coecet L[ ;; beg abta cotat eal o cole Tag the euato 3 educe to the well ow geeal cla o oloal S [ due to Sataa [3 58 e II a Itegal The ollowg tegal coceg the bothogoal oloal wth ceta oduct o ecal ucto hae bee deed the ae a Ft Itegal co u h ; α N a e H [ b H S [ d [ / [ / φ h Γ ± u / Note b a b a Γα Global Joual Ic S
L [ ;; Note H λ : u;; u A C :BD;;B D [ V h ξ ξ : ξ [ c: > [ a: u [ ± h ξ ξ : ξ whee [ b: φ;;[b :φ ; [ d: δ;;[d :δ ; d u ;Re V > ; u δ > T > ag < Tπ T > ag T π > < < to 4 ae o-eo abta ote tege ad the coecet L [ ; ; ae abta cotat eal o cole b Secod Itegal H co u co N co a b co e h ; H co co [ co α 3 Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I S [ co co d Global Joual Ic S
[ / / 4 Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I H λ : u;;u AC :BD;;B D whee u φ [ b: φ;;[b :φ ; [ d: δ;;[d :δ ; πγ u h [ [ : u [ c: ± h - : : 5 b Re V T > ag < T π T > ag < T π d δ > > < ; u < h > ae o-eo abta ote tege ad the coecet L[ ae abta cotat eal o cole oo o 4 Eeg the oloal a ge Fo H-ucto ee the geealed ultaable oloal b 3 -ee ad the H-ucto o eeal cole aable ell - Bae cotou tegal b chagg the ode o tegato ad uato whch eal ee to be uted due to the abolute coegece o the tegal ad the uato oled the oce ad the ealuatg the eultg tegal wth the hel o the ollowg eult ; Note π/ co u Γ Γ ± u d u Γ ± 6 Global Joual Ic S
whee u ad Re > Fall teetg the eult thu obtaed wth the hel o we ae at the eued eult 3 The tegal o 3 to 34 ca alo be obtaed the la ae wth the hel o the aoate tegal 35 ad the ollowg eult Note π/ whee u ad Re > co u co d πγ u u Γ ± 7 III Secal Cae 5 uttg λ A u B D D H co u N α [ a b e S h ; [ 4 we d A : B;;B [ a: :[ b: φ;;[ b :φ ; F d B: D;;D [ c: :[ d: δ;;[-d :δ ; [ / / Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I φ b b a a Γα Γ ± u h Global Joual Ic S
F A :B;;B C :D;;D [ h : ξ [ c: : [ a: u [ ± h : [ b: φ;;[b :φ ; [ d: δ;;[d :δ ; 8 Note 6 Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I b oded that u Re > ag < T π T > ad the ee o the ght o 8 abolutel coeget Tag the eult 8 educe to the ollowg tegal H N co u a b e S h ; [ A : B;B [ a: :[ b: φ;;[ b :φ ; S B: D;D [ c: :[ d: δ;;[-d :δ ; α [ d [ / / d φ a Γ ± u h a Global Joual Ic S
Note S A :B;;B C :D;;D [ h : [ c: [ a: u [ ± h [ b: φ;[b :φ ; : [ d: δ;[d :δ ; 9 b whee u Re > ; ag < T π T > ad the ee o the ght o 9 coege abolutel Lettg λ A C 4 we get co u h ; a e α N H b [ S u [ :φ H b d [ d :δ B D [ / / 7 Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I φ Γ ± u h a a b b γα Global Joual Ic S
H :u;;u :BD;;B D [ h [ c: : [ a: u [ ± h [ b: φ;;[b :φ ; : [ δ :δ d: ;;[d ; Note 8 Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I ald ude the ae codto a obtaable o eult 4 Settg euato 4 we d co u h ; a e α N H b [ S λ: u ; u [ a: :[ b: φ;[ b :φ ; H d AC:BD;B D [ c: :[ d: δ;[d :δ ; [ / / φ Γ ± u h a a b b γα Global Joual Ic S
Note whee H λ :u;u A C :BD;B D [ a: u [ ± h u T T [ h : : [ c: u Re [ b: φ ;[ b : φ : ξ ξ : [ d: δ;[d :δ ; b d δ > ag < T π ag d δ > u < T π; ag < πtt > > < < h > ae ote coecet ad L ae abta cotat eal o cole Tag λ A B D D co u co co h ; a e α N H co b [ co S co co 5 we get 9 Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I F A : B;;B B: D;;D [ a: :[ b: φ;;[ b :φ ; [ c: :[ d: δ;;[-d :δ ; co co d Global Joual Ic S
[ / / φ b a b a Γα πγ u h Note Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I F A :B;;B C :D;;D [ b: φ;;[ b : φ ; [ d: δ;;[ d :δ ; oded [ a: :[ u [ c: : ± h e e b u Re > ag < T π T > < < ad the ee o the ght o coege abolutel uttg we obta co u co co h ; a e α N H co b [ co S co co Global Joual Ic S
A : B;B [ a: :[ b: φ;[ b :φ ; S co co B: D;D [ c: :[ d: δ;[ d :δ ; d Note / φ [ / S A :B;B C :D;D [ b: φ;[ b : φ ; [ d: δ;[ d :δ; oded that πγ u h b a [ a: :[ u [ c: : ± h b : a Γα b u Re > ag < T π T > ad the ee o the ght o 3 abolutel coeget 3 Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I Lettg λ A C 5 we hae co u co co h ; Global Joual Ic S
a e α N H co b [ co S co co H u B D co [ b :φ [ d :δ d Note Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I H φ : u;;u :BD;;B [ b: φ;;[b :φ ; [ d: δ;;[d :δ ; D [ / Γ u h b a / b a [ a: :[ : u [ c: ± h - : 4 ald ude the ae codto a tated o 5 uttg 5 we get Γα co u co co h ; Global Joual Ic S
Global Joual Ic S 3 Global Joual o Scece Fote Reeach Volue XII Iue eo I V XI F e a b N co H [ α co co co S ; :φ φ :[ [ ; :δ δ :[ [ λ: d co co H b ;[ b: a: ;[d d: c: u u ; D AC:BD;B / φ h u / [ πγ b b a a Γα :[ : [ : ± [ : a: - h u c: u;;u D :BD;;B H ; :φ φ [ ; :δ δ [ ;;[b b: ;;[d d: 5 whee u; ; d d b Re u > δ δ Note
4 Global Joual o Scece Fote Reeach F Volue XII Iue XI V eo I u ; ag < > T π T T T > < < h > Reeece Rééece Reeeca to Bhatt KN Itegal olg ceta oduct o bothogoal oloal ad the H-ucto V Au at 3 987 7-34 Baaa BLJ Atotc eao ad aaltc cotuato o a cla o a Bae tegal Co ath 5 963 339-34 3 Chauaa VBL Ceta tegal oete etag to ecal ucto Sceta See A ath Sc 9-6 4 Chauaa VBL ad Aghot ueh The oduct o geealed oloal et etag to a cla o cooluto tegal euato Deo ath XLII 3 9 55-5 5 Fo C The G ad H-ucto a etcal Foue eel Ta Ae ath Soc 98 96 395-49 6 ttal K ad Guta KC A tegal olg geealed ucto o two aable oc Id Acad Sco 75A 97 7-3 7 abhaa TR ad Toa RC Soe tegal ad ee elato o bothogoal oloal uggeted b the Legede oloal Ida J ue al ath 7 98 863-869 8 Sataa H ad Daout C Ceta geealed Neua eao aocated wth the Kaé de Féet ucto Ned Aad Wet oc Se A 7 Id ath 3 969 449-457 9 Sataaa H ad Daout C Soe geeatg ucto o the Jacob oloal Coet ath St aul 97 5- Sataa H ad ada R Eao theoe o the H-ucto o eeal cole aable J Ree Agew ath 88 976 9-45 Sataa H ad ada R Soe blateal geeatg ucto o a cla o geealed hegeoetc oloal J Ree Agew ath 83/84 97 65-74 Sataa H A ultlea geeatg ucto o the Kohaue et o bothogoal oloal uggeted b Laguee oloal acc J ath 7 985 83-9 3 A cotou tegal olg Fo ucto Ida J ath 4 97-6 4 Sb Soe eao theoe o the H-ucto A olo ath 3 97 5-38 5 Shaa Factoal tegato ad actoal deetato o the -See Factoal Calculu Al Aal 8 88-9 Note Global Joual Ic S