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

7.33 Combinations of the polynomials Cnv(x)si438_e and Bessel functions. Integration of Gegenbauer functions with respect to the index

7.331

1. 

1x2n+1v(x21)v2n12C2nv2n(1x)Jv(xy)dx=(1)n22nv+1yv+2n1[(2n)!]1Γ(2v2n)[Γ(v2n)]1cosy

si439_e  ET II 44(10)a

[y>0,2n12<Rev<2n+12]si440_e

7.332

1. 

0xv+1?(x2+β2)12v34C2n+1v+12[(x2+β2)1/2β]?Jv+32+2n[(x2+β2)1/2a]?Jv(xy)dx=(1)n21/2π1/2a12vyv(a2y2)1/2sin[β(a2y2)1/2]C2n+1v+12[(1y2a2)1/2][0<y<a]=0

  ET II 59(23) ...

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