DLMF:10.22.E6

MaRDI QIDQ4076

• Label: DLMF:10.22.E6

Digital Library of Mathematical Functions ID 10.22.E6

${\displaystyle{\displaystyle\int\mathscr{C}_{\mu}\left(az\right)\mathscr{D}_{\nu}(az)\frac{\mathrm{d}z}{z}=-\frac{az(\mathscr{C}_{\mu+1}\left(az\right)\mathscr{D}_{\nu}(az)-\mathscr{C}_{\mu}\left(az\right)\mathscr{D}_{\nu+1}(az))}{\mu^{2}-\nu^{2}}+\frac{\mathscr{C}_{\mu}\left(az\right)\mathscr{D}_{\nu}(az)}{\mu+\nu},}}$

Constraint(s)

${\displaystyle{\displaystyle\mu^{2}\neq\nu^{2}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: 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
• ${\displaystyle{\displaystyle\mathscr{D}_{\nu}(z)}}$: cylinder function
 

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