# DLMF:11.5.E1 (Q3968)

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DLMF:11.5.E1
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## Statements

${\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right)=\frac{2(\tfrac{1}{2% }z)^{\nu}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{1}{2}\right)}\int_{0}^{1}(1-t^{2})% ^{\nu-\frac{1}{2}}\sin\left(zt\right)\mathrm{d}t=\frac{2(\tfrac{1}{2}z)^{\nu}}% {\sqrt{\pi}\Gamma\left(\nu+\tfrac{1}{2}\right)}\int_{0}^{\pi/2}\sin\left(z\cos% \theta\right)(\sin\theta)^{2\nu}\mathrm{d}\theta,}}$
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DLMF:11.5.E1
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${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}$
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${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$
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${\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}$
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${\displaystyle{\displaystyle\pi}}$
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${\displaystyle{\displaystyle\cos\NVar{z}}}$
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${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$
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${\displaystyle{\displaystyle\int}}$
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${\displaystyle{\displaystyle\Re}}$
${\displaystyle{\displaystyle\sin\NVar{z}}}$
${\displaystyle{\displaystyle z}}$
${\displaystyle{\displaystyle\nu}}$