Formula:10370

Digital Library of Mathematical Functions ID 33.20.E9

${\displaystyle{\displaystyle{\sf H}_{k}(\ell;r)=(-1)^{\ell+1}\frac{2}{\pi}\sum_{p=2k}^{3k}(2|r|)^{(p+1)/2}C_{k,p}K_{2\ell+1+p}\left(\sqrt{8|r|}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle r<0}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle r}}$: real variable
• ${\displaystyle{\displaystyle C_{k,p}}}$: coefficients
• ${\displaystyle{\displaystyle\mathsf{H}_{k}(\ell;r)}}$: coefficient
 

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