DLMF:13.14.E28 (Q4520): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
test:

W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperW{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E3.m2apdec

Revision as of 15:07, 2 January 2020

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DLMF:13.14.E28
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    Statements

    test
    𝒲 ⁡ { M κ , - μ ⁡ ( z ) , W κ , μ ⁡ ( z ) } = - Γ ⁡ ( 1 - 2 ⁢ μ ) Γ ⁡ ( 1 2 - μ - κ ) , Wronskian Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 Euler-Gamma 1 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 {\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,-\mu}\left(z\right),W_% {\kappa,\mu}\left(z\right)\right\}=-\frac{\Gamma\left(1-2\mu\right)}{\Gamma% \left(\frac{1}{2}-\mu-\kappa\right)},}}
    0 references
    DLMF id
    DLMF:13.14.E28
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2akdec
    0 references
    Whittaker confluent hypergeometric function
    test
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2amdec
    0 references
    Whittaker confluent hypergeometric function
    test
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2apdec
    0 references
     
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