Formula:4649

Digital Library of Mathematical Functions ID 11.4.E20

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \StruveH{\nu}@{z}=\frac{(\tfrac{1}{2}z)^{\nu+\frac{1}{2}}}{\EulerGamma@{\nu+\tfrac{1}{2}}}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(k+\nu+\tfrac{1}{2})}\BesselJ{k+\frac{1}{2}}@{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
• ${\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Struve function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: real or complex order
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
 

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