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

$\underset{0}{\overset{\infty }{\int }}x{(x^2+b^2)}^{-\frac{1}{2}v}\text{?}\text{?}{\mathit{K}}_{\pm v}(a\sqrt{x^2+b^2})\text{?}sin(cx)\text{d}x=\sqrt{\frac{\pi }{2}{a}^v{b}^{v+\frac{3}{2}}c{(a^2+c^2)}^{-\frac{1}{2}v-\frac{3}{4}}\text{?}{\mathit{K}}_{-v-\frac{3}{2}}(b\sqrt{a^2-c^2})}\text{?}$

  ET I 113(45)

$\text{?}[Rea>0,\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}Reb>0,\text{?}\text{?}\text{?}\text{?}\text{?}c>0]$

4¹¹. 

$\underset{0}{\overset{\infty }{\int }}x{(x^2+b^2)}^{\mp \frac{1}{2}v}\text{?}\text{?}{\mathit{K}}_{\pm v}(a\sqrt{x^2+b^2})\text{?}cos(cx)\text{d}x=\sqrt{\frac{\pi }{2}{a}^{\mp v}{b}^{\frac{1}{2}v\mp }\text{?}{(a^2+c^2)}^{\pm \frac{1}{2}v-\frac{1}{4}}\text{?}{\mathit{K}}_{\pm v-\frac{1}{2}}(b\sqrt{a^2+c^2})}\text{?}$

  ET I 56(45)

$\text{?}\text{?}[Rea>0,\text{?}\text{?}\text{?}\text{?}\text{?}\text{?}Reb>0,\text{?}\text{?}\text{?}\text{?}\text{?}c\text{?}\text{?}\text{is}\text{?}\text{real}]\text{?}$

5. 

$\begin{array}{l}\underset{0}{\overset{\infty }{\int }}x{(x^2+a^2)}^{-\frac{1}{2}v}\text{?}\text{?}{Y}_v(b\sqrt{x^2+a^2})\text{?}cos(cx)\text{d}x=\sqrt{\frac{a\pi }{2}{(ab)}^{-v}\text{?}{(b^2-c^2)}^{\frac{1}{2}v-\frac{1}{4}}\text{?}{Y}_{v-\frac{1}{2}}\text{?}(a\sqrt{b^2-c^2})}\hfill \end{array}$