Table of Integrals, Series, and Products, 8th Edition

6.78 Combinations of Bessel and other special functions

6.781

$\begin{array}{ccc}{\displaystyle {\int }_0^{\infty }si(ax)J_0(bx)\text{d}x}& =-\frac{1}{b}\arcsin \left(\frac{b}{a}\right)& [0<b<a]\\ =0& [0<a<b]\end{array}$

  ET II 13(6)

6.782

1. 

${\displaystyle {\int }_0^{\infty }\text{Ei}(-x)J_0(2\sqrt{zx})\text{d}x=\frac{e^{-z}-1}{z}}$

  NT 60(4)

2. 

${\displaystyle {\int }_0^{\infty }\text{si}(x)J_0(2\sqrt{zx})\text{d}x=-\frac{sinz}{z}}$

  NT 60(6)

3. 

${\displaystyle {\int }_0^{\infty }\text{ci}(x)J_0(2\sqrt{zx})\text{d}x=\frac{cosz-1}{z}}$

  NT 60(5)

4. 

${\displaystyle {\int }_0^{\infty }\text{Ei}(-x)J_1(2\sqrt{zx})\frac{\text{d}x}{\sqrt{x}}=\frac{\text{Ei}(-z)-C-lnz}{\sqrt{z}}}$

  NT 60(7)

5. 

${\displaystyle {\int }_0^{\infty }\text{si}(x)J_1(2\sqrt{zx})\frac{\text{d}x}{\sqrt{x}}=-\frac{\frac{\pi }{2}-si(z)}{\sqrt{z}}}$

  NT 60(9) ...