Formula:4698

Digital Library of Mathematical Functions ID 11.7.E11

${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu-\nu-1}\mathbf{H}_{\nu}\left(t\right)\mathrm{d}t=\frac{\Gamma\left(\tfrac{1}{2}\mu\right)2^{\mu-\nu-1}\tan\left(\tfrac{1}{2}\pi\mu\right)}{\Gamma\left(\nu-\tfrac{1}{2}\mu+1\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle|\Re\mu|<1}}$
${\displaystyle{\displaystyle\Re\nu>\Re\mu-\tfrac{3}{2}}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Struve function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\tan\NVar{z}}}$: tangent function
• ${\displaystyle{\displaystyle\nu}}$: real or complex order
 

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