Formula:10224

Digital Library of Mathematical Functions ID 33.5.E9

${\displaystyle{\displaystyle C_{\ell}\left(\eta\right)\sim\dfrac{e^{-\pi\eta/2}}{(2\ell+1)!!}\sim e^{-\pi\eta/2}\dfrac{e^{\ell}}{\sqrt{2}(2\ell)^{\ell+1}}.}}$

Symbols List

• ${\displaystyle{\displaystyle C_{\NVar{\ell}}\left(\NVar{\eta}\right)}}$: normalizing constant for Coulomb radial functions
• ${\displaystyle{\displaystyle\sim}}$: asymptotic equality
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle!!}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle\eta}}$: real parameter
 

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