Formula:5297

Digital Library of Mathematical Functions ID 13.20.E11

${\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\left(\tfrac{1}{2}\mu\right)^{-\frac{1}{4}}\*\left(\frac{\kappa+\mu}{e}\right)^{\frac{1}{2}(\kappa+\mu)}\*\Phi(\kappa,\mu,x)\*U\left(\mu-\kappa,\zeta\sqrt{2\mu}\right)\left(1+O\left(\mu^{-1}\ln\mu\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\Phi(\kappa,\mu,x)}}$: function (locally)
 

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