Plot of the <a href="https://en.wikipedia.org/wiki/Struve_function" class="extiw" title="en:Struve function">Struve function</a> H<sub>n</sub>(<i>x</i>) in the interval [−12,12] for <i>n</i> in [0, 1, 2, 3, 4]
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {H} _{n}(x)=\sum _{m=0}^{\infty }{\frac {(-1)^{m}}{\Gamma \left(m+{\frac {3}{2}}\right)\Gamma \left(m+n+{\frac {3}{2}}\right)}}\left({\frac {x}{2}}\right)^{2m+n+1}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">H</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><munderover><mo>∑<!-- ∑ --></mo><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mo>=</mo><mn>0</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">∞<!-- ∞ --></mi></mrow></munderover><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mo stretchy="false">(</mo><mo>−<!-- − --></mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mi>m</mi></mrow></msup></mrow><mrow><mi mathvariant="normal">Γ<!-- Γ --></mi><mrow><mo>(</mo><mrow><mi>m</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></mrow><mo>)</mo></mrow><mi mathvariant="normal">Γ<!-- Γ --></mi><mrow><mo>(</mo><mrow><mi>m</mi><mo>+</mo><mi>n</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></mrow><mo>)</mo></mrow></mrow></mfrac></mrow><msup><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>x</mi><mn>2</mn></mfrac></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mi>m</mi><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \mathbf {H} _{n}(x)=\sum _{m=0}^{\infty }{\frac {(-1)^{m}}{\Gamma \left(m+{\frac {3}{2}}\right)\Gamma \left(m+n+{\frac {3}{2}}\right)}}\left({\frac {x}{2}}\right)^{2m+n+1}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bbb5f4ca26fd37fc89e72d1e8ea256c63f09d2d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -4.505ex; width:53.048ex; height:8.343ex;" alt="{\displaystyle \mathbf {H} _{n}(x)=\sum _{m=0}^{\infty }{\frac {(-1)^{m}}{\Gamma \left(m+{\frac {3}{2}}\right)\Gamma \left(m+n+{\frac {3}{2}}\right)}}\left({\frac {x}{2}}\right)^{2m+n+1}}"></span></dd></dl>
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