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

  ET II 80(26)

$[y>0,|\arg a|<\frac{3}{4}\pi ,\mathrm{Re}\mu <-\mathrm{Re}\lambda <\mathrm{Re}\nu +\frac{3}{2}]$

15. 

${\displaystyle \underset{0}{\overset{\infty }{\int }}{x}^{\nu +1}{e}^{\frac{1}{4}{x}^2}{D}_{-2\nu -1}(x)\text{?}{J}_{\nu }\text{(}xy\text{)d}x}=(2\nu +1)y^{\nu -1}{e}^{\frac{1}{4}{y}^2}{D}_{-2\nu -2}(y)$

  ET II 79(20)

$[y>0,\mathrm{Re}\nu >-\frac{1}{2}]$

16. 

${\displaystyle \underset{0}{\overset{\infty }{\int }}{x}^{\nu +1}{e}^{-\frac{1}{4}{x}^2}{D}_{-2\nu -3}(x)\text{?}{J}_{\nu }\text{(}xy\text{)d}x}=2^{-1/2}{\pi }^{1/2}{y}^{-\nu -2}{e}^{-\frac{1}{4}{y}^2}{I}_{\nu +1}(\frac{1}{4}{y}^2)$

  ET II 79(21)

$[y>0,\text{?}\text{?}\mathrm{Re}\nu >-1]$

17. 

${\displaystyle \underset{0}{\overset{\infty }{\int }}}$