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DLMF:10.22#Ex5 - MaRDI portal

DLMF:10.22#Ex5 (Q4077)

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DLMF:10.22#Ex5
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    Statements

    DLMF defining formula
    ∫ z μ + ν + 1 ⁢ 𝒞 μ ⁡ ( a ⁢ z ) ⁢ 𝒟 ν ⁢ ( a ⁢ z ) ⁢ d z = z μ + ν + 2 2 ⁢ ( μ + ν + 1 ) ⁢ ( 𝒞 μ ⁡ ( a ⁢ z ) ⁢ 𝒟 ν ⁢ ( a ⁢ z ) + 𝒞 μ + 1 ⁡ ( a ⁢ z ) ⁢ 𝒟 ν + 1 ⁢ ( a ⁢ z ) ) , superscript 𝑧 𝜇 𝜈 1 cylinder-function 𝜇 𝑎 𝑧 subscript 𝒟 𝜈 𝑎 𝑧 𝑧 superscript 𝑧 𝜇 𝜈 2 2 𝜇 𝜈 1 cylinder-function 𝜇 𝑎 𝑧 subscript 𝒟 𝜈 𝑎 𝑧 cylinder-function 𝜇 1 𝑎 𝑧 subscript 𝒟 𝜈 1 𝑎 𝑧 {\displaystyle{\displaystyle\int z^{\mu+\nu+1}\mathscr{C}_{\mu}\left(az\right)% \mathscr{D}_{\nu}(az)\mathrm{d}z=\frac{z^{\mu+\nu+2}}{2(\mu+\nu+1)}\*\left(% \mathscr{C}_{\mu}\left(az\right)\mathscr{D}_{\nu}(az)+\mathscr{C}_{\mu+1}\left% (az\right)\mathscr{D}_{\nu+1}(az)\right),}}
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    constraint
    μ + ν ≠ - 1 𝜇 𝜈 1 {\displaystyle{\displaystyle\mu+\nu\neq-1}}
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    Identifiers

     
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