Formula:3880

Digital Library of Mathematical Functions ID 10.17.E13

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \rselection{\HankelH{1}{\nu}@{z}\\ \HankelH{2}{\nu}@{z}}=\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{\pm i\omega}\left(\sum_{k=0}^{\ell-1}(\pm i)^{k}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}^{\pm}(\nu,z)\right),}

Constraint(s)

${\displaystyle{\displaystyle\ell=1,2,\ldots}}$

Symbols List

• ${\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$: Bessel function of the third kind (or Hankel function)
• ${\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$: Bessel function of the third kind (or Hankel function)
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle a_{k}(\nu)}}$: expansion (locally)
• ${\displaystyle{\displaystyle\omega}}$: 10.17.E2
• ${\displaystyle{\displaystyle R_{\ell}^{\pm}(\nu,z)}}$: remainder (locally)
 

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