O'Reilly logo

Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

7.54 Combinations of hypergeometric and Bessel functions

7.541

0xα+β2ν1(x+1)νexzKν[(x+1)z]F(α,β;α+β2ν;x)dx=π12cos(νπ)Γ(12α+ν)Γ(12β+ν)Γ(γ)(2z)1212γW12λ,12(βα)(2z)

si680_e  ET II 401(16)

γ=α+β2ν[Re(α+β2ν)>0,Re(12α+υ)>0,Re(12β+υ)>0,|argz|<32π]si681_e

7.542

1.12 

0xσ1Fpp1(a1,,ap;b1,,bp1;λx2)Yν(xy)dx=Γ(b1)Γ(bp1)2λ12σΓ(a1)Γ(ap)Gp+2,p+3p+2,1(y24λ|b0*,,bp1*,lh,k,a1*,,ap*,l)

si682_e  ET II 118(53)

aj*=ajσ2,j=1,,p;b0*=1σ2;bj*=bjσ2,j=1,,p

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required