DLMF:10.22#Ex6 (Q3381): Difference between revisions

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Property / constraint
 

μ + ν 1 𝜇 𝜈 1 {\displaystyle{\displaystyle\mu+\nu\neq 1}}

\mu+\nu\neq 1
Property / constraint: μ + ν 1 𝜇 𝜈 1 {\displaystyle{\displaystyle\mu+\nu\neq 1}} / rank
 
Normal rank

Latest revision as of 16:18, 30 December 2019

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DLMF:10.22#Ex6
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    Statements

    z - μ - ν + 1 𝒞 μ ( a z ) 𝒟 ν ( a z ) d z = z - μ - ν + 2 2 ( 1 - μ - ν ) ( 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 1 𝜇 𝜈 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(1-\mu-\nu)}\*\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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    μ + ν 1 𝜇 𝜈 1 {\displaystyle{\displaystyle\mu+\nu\neq 1}}
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