### 6.78 Combinations of Bessel and other special functions

6.781

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

ET II 13(6)

6.782

1.

$\int}_{0}^{\infty}\text{Ei}(-x){J}_{0}(2\sqrt{zx})\text{d}x=\frac{{e}^{-z}-1}{z$

NT 60(4)

2.

$\int}_{0}^{\infty}\text{si}(x){J}_{0}(2\sqrt{zx})\text{d}x=-\frac{sinz}{z$

NT 60(6)

3.

$\int}_{0}^{\infty}\text{ci}(x){J}_{0}(2\sqrt{zx})\text{d}x=\frac{cosz-1}{z$

NT 60(5)

4.

$\int}_{0}^{\infty}\text{Ei}(-x){J}_{1}(2\sqrt{zx})\frac{\text{d}x}{\sqrt{x}}=\frac{\text{Ei}(-z)-C-lnz}{\sqrt{z}$

NT 60(7)

5.

$\int}_{0}^{\infty}\text{si}(x){J}_{1}(2\sqrt{zx})\frac{\text{d}x}{\sqrt{x}}=-\frac{\frac{\pi}{2}-si(z)}{\sqrt{z}$

NT 60(9) ...

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