Formula:5328

Digital Library of Mathematical Functions ID 13.21.E23

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{x}=\sqrt{2\pi}\kappa^{\frac{1}{6}}\*\left(\frac{\kappa+\mu}{\kappa-\mu}\right)^{\frac{1}{2}\mu}\*\left(\frac{\kappa^{2}-\mu^{2}}{e^{2}}\right)^{\frac{1}{2}\kappa}\*\widehat{\Psi}(\kappa,\mu,x)\*\left(\AiryAi@{\kappa^{\frac{2}{3}}\widehat{\zeta}}+\envAiryAi@{\kappa^{\frac{2}{3}}\widehat{\zeta}}\bigO@{\kappa^{-1}}\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
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \cpi} : the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{envAi}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\widehat{\Psi}(\kappa,\mu,x)}}$: function (locally)
 

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