Formula:4647

Digital Library of Mathematical Functions ID 11.4.E18

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \StruveH{\nu}@{z}=\frac{4}{\pi^{1/2}\EulerGamma@{\nu+\tfrac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{(2k+\nu+1)\EulerGamma@{k+\nu+1}}{k!(2k+1)(2k+2\nu+1)}\BesselJ{2k+\nu+1}@{z},}

Constraint(s)

${\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}$

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
• ${\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Struve function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: real or complex order
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
 

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