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

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6.61 Combinations of Bessel functions and exponentials

6.611

1. 

0eαxJv(bx)dx=bv[α2+b2α]vα2+b2[Rev>1,?Re(α±ib)>0]

si958_e  EH II 49(18), WA 422(8)

2. 

0eαxYv(bx)dx=(α2+b2)12cosec(vπ)×{bv[(α2+b2)12+α]vcos(vπ)bv[(α2+b2)12+α]v}

si959_e  MO 179, ET II 105(1)

[Reα>0,?b>0,?|Rev|<1]si960_e

3. 

0eαxKv(bx)dx=πbsin(vπ)sin(vθ)sinθ

si961_e  ET II 131(22)

[cosθ=αb;?with ...

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