Formula:4650

Digital Library of Mathematical Functions ID 11.4.E21

${\displaystyle{\displaystyle\mathbf{H}_{0}\left(z\right)=\frac{4}{\pi}\sum_{k=0}^{\infty}\frac{J_{2k+1}\left(z\right)}{2k+1}=2\sum_{k=0}^{\infty}(-1)^{k}{J_{k+\frac{1}{2}}^{2}}\left(\tfrac{1}{2}z\right),}}$

Symbols List

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

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