Formula:4071

Digital Library of Mathematical Functions ID 10.22.E2

${\displaystyle{\displaystyle\int z^{\nu}\mathscr{C}_{\nu}\left(z\right)\mathrm{d}z=\pi^{\frac{1}{2}}2^{\nu-1}\Gamma\left(\nu+\tfrac{1}{2}\right)\*z\left(\mathscr{C}_{\nu}\left(z\right)\mathbf{H}_{\nu-1}\left(z\right)-\mathscr{C}_{\nu-1}\left(z\right)\mathbf{H}_{\nu}\left(z\right)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\nu\neq-\tfrac{1}{2}}}$

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
• ${\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: cylinder function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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