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) ...

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