Formula:10308

Digital Library of Mathematical Functions ID 33.14.E7

${\displaystyle{\displaystyle h\left(\epsilon,\ell;r\right)=\frac{\Gamma\left(\ell+1-\kappa\right)}{\pi\kappa^{\ell}}\left(W_{\kappa,\ell+\frac{1}{2}}\left(2r/\kappa\right)+(-1)^{\ell}S(\epsilon,r)\frac{\Gamma\left(\ell+1+\kappa\right)}{2(2\ell+1)!}M_{\kappa,\ell+\frac{1}{2}}\left(2r/\kappa\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle r}}$: real variable
• ${\displaystyle{\displaystyle\epsilon}}$: real parameter
• ${\displaystyle{\displaystyle\kappa}}$: quantity (locally)
• ${\displaystyle{\displaystyle S(\epsilon,r)}}$: function (locally)
 

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