6.78 Combinations of Bessel and other special functions

6.781

$\begin{array}{ccc}{\int }_{0}^{\infty }si\left(ax\right){J}_{0}\left(bx\right)\text{d}x& =-\frac{1}{b}\mathrm{arcsin}\left(\frac{b}{a}\right)& \left[0 ET II 13(6)

6.782

1.

${\int }_{0}^{\infty }\text{Ei}\left(-x\right){J}_{0}\left(2\sqrt{zx}\right)\text{d}x=\frac{{e}^{-z}-1}{z}$ NT 60(4)

2.

${\int }_{0}^{\infty }\text{si}\left(x\right){J}_{0}\left(2\sqrt{zx}\right)\text{d}x=-\frac{sinz}{z}$ NT 60(6)

3.

${\int }_{0}^{\infty }\text{ci}\left(x\right){J}_{0}\left(2\sqrt{zx}\right)\text{d}x=\frac{cosz-1}{z}$ NT 60(5)

4.

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

NT 60(7)

5.

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

NT 60(9) ...

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