DLMF:10.22.E6 (Q3379): Difference between revisions

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Property / constraint
 

μ 2 ν 2 superscript 𝜇 2 superscript 𝜈 2 {\displaystyle{\displaystyle\mu^{2}\neq\nu^{2}}}

\mu^{2}\neq\nu^{2}
Property / constraint: μ 2 ν 2 superscript 𝜇 2 superscript 𝜈 2 {\displaystyle{\displaystyle\mu^{2}\neq\nu^{2}}} / rank
 
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Revision as of 16:18, 30 December 2019

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DLMF:10.22.E6
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    Statements

    𝒞 μ ( a z ) 𝒟 ν ( a z ) d z z = - a z ( 𝒞 μ + 1 ( a z ) 𝒟 ν ( a z ) - 𝒞 μ ( a z ) 𝒟 ν + 1 ( a z ) ) μ 2 - ν 2 + 𝒞 μ ( a z ) 𝒟 ν ( a z ) μ + ν , cylinder-function 𝜇 𝑎 𝑧 subscript 𝒟 𝜈 𝑎 𝑧 𝑧 𝑧 𝑎 𝑧 cylinder-function 𝜇 1 𝑎 𝑧 subscript 𝒟 𝜈 𝑎 𝑧 cylinder-function 𝜇 𝑎 𝑧 subscript 𝒟 𝜈 1 𝑎 𝑧 superscript 𝜇 2 superscript 𝜈 2 cylinder-function 𝜇 𝑎 𝑧 subscript 𝒟 𝜈 𝑎 𝑧 𝜇 𝜈 {\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},}}
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    μ 2 ν 2 superscript 𝜇 2 superscript 𝜈 2 {\displaystyle{\displaystyle\mu^{2}\neq\nu^{2}}}
    0 references