Formula:5309

Digital Library of Mathematical Functions ID 13.21.E4

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \WhittakerconfhyperW{-\kappa}{\mu}@{xe^{\pi\iunit}}=\frac{\pi\sqrt{x}}{\EulerGamma@{\kappa+\tfrac{1}{2}}}e^{-\mu\pi\iunit}\*\left(\HankelH{2}{2\mu}@{2\sqrt{x\kappa}}+\envBesselY{2\mu}@{2\sqrt{x\kappa}}\bigO@{\kappa^{-\frac{1}{2}}}\right),}

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$: Bessel function of the third kind (or Hankel function)
• ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle x}}$: real variable
 

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