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Modified Struve Function

TOP/Special functions/Struve function
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Calculate the value of the modified Struve function Lv(x).
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\(\normalsize Modified\ Struve\ function\ L_\nu(x)\\ (1)\ x^2y''+xy'-(x^2+\nu^2)y={\large\frac{4({\large\frac{x}{2}})^{\nu +1}}{{\large\sqrt\pi}\Gamma(\nu+\frac{1}{2})}} \\ \hspace{25px} y=L_\nu(x)\\ (2)\ L_\nu(x)={\large(\frac{x}{2})^{\nu +1}}{\large\displaystyle \sum_{\small k=0}^{\small\infty}\frac{({\large\frac{x}{2}})^{2k}}{\Gamma(k+\frac{3}{2})\Gamma(k+\nu+\frac{3}{2})}} \\\)

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