Formula:10190

Digital Library of Mathematical Functions ID 33.2.E3

${\displaystyle{\displaystyle F_{\ell}\left(\eta,\rho\right)=C_{\ell}\left(\eta\right)2^{-\ell-1}(\mp\mathrm{i})^{\ell+1}M_{\pm\mathrm{i}\eta,\ell+\frac{1}{2}}\left(\pm 2\mathrm{i}\rho\right),}}$

Symbols List

• ${\displaystyle{\displaystyle C_{\NVar{\ell}}\left(\NVar{\eta}\right)}}$: normalizing constant for Coulomb radial functions
• ${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle\rho}}$: nonnegative real variable
• ${\displaystyle{\displaystyle\eta}}$: real parameter
 

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