DLMF:10.22.E4

MaRDI QIDQ4074

• Label: DLMF:10.22.E4

Digital Library of Mathematical Functions ID 10.22.E4

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

Constraint(s)

${\displaystyle{\displaystyle a^{2}\neq b^{2}}}$

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

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