Formula:5329

Digital Library of Mathematical Functions ID 13.21.E24

${\displaystyle{\displaystyle W_{-\kappa,\mu}\left(xe^{-\pi\mathrm{i}}\right)=e^{(\kappa-\frac{1}{6})\pi\mathrm{i}}\widehat{c}(\kappa,\mu)\widehat{\Psi}(\kappa,\mu,x)\left(\mathrm{Ai}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}e^{-\frac{2}{3}\pi\mathrm{i}}\right)+\mathrm{envBi}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}\right)O\left(\kappa^{-1}\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{envBi}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\widehat{c}(\kappa,\mu)}}$: function (locally)
• ${\displaystyle{\displaystyle\widehat{\Psi}(\kappa,\mu,x)}}$: function (locally)
 

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