Formula:4713

Digital Library of Mathematical Functions ID 11.9.E8

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \Lommels{\mu}{\nu}@{z}=2^{(\mu+\nu-1)/2}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}z^{(\mu+1-\nu)/2}\*\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(2k+\mu-\nu+1)}\BesselJ{k+\frac{1}{2}(\mu+\nu+1)}@{z}.}

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle s_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right)}}$: Lommel function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: real or complex order
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
 

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