Formula:4712

Digital Library of Mathematical Functions ID 11.9.E7

${\displaystyle{\displaystyle s_{{\mu},{\nu}}\left(z\right)=2^{\mu+1}\sum_{k=0}^{\infty}\*\frac{(2k+\mu+1)\Gamma\left(k+\mu+1\right)}{k!(2k+\mu-\nu+1)(2k+\mu+\nu+1)}J_{2k+\mu+1}\left(z\right),}}$

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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