DLMF:13.15.E21 (Q4546): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
Defining formula:

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.m2agdec

Revision as of 16:09, 2 January 2020

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DLMF:13.15.E21
No description defined

    Statements

    Defining formula
    d n d z n ⁡ ( e 1 2 ⁢ z ⁢ z - μ - 1 2 ⁢ W κ , μ ⁡ ( z ) ) = ( - 1 ) n ⁢ ( 1 2 + μ - κ ) n ⁢ e 1 2 ⁢ z ⁢ z - μ - 1 2 ⁢ ( n + 1 ) ⁢ W κ - 1 2 ⁢ n , μ + 1 2 ⁢ n ⁡ ( z ) , derivative 𝑧 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜇 1 2 Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 superscript 1 𝑛 Pochhammer 1 2 𝜇 𝜅 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜇 1 2 𝑛 1 Whittaker-confluent-hypergeometric-W 𝜅 1 2 𝑛 𝜇 1 2 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {\frac{1}{2}z}z^{-\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}% {\left(\tfrac{1}{2}+\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}(% n+1)}\*W_{\kappa-\frac{1}{2}n,\mu+\frac{1}{2}n}\left(z\right),}}
    0 references
    DLMF id
    DLMF:13.15.E21
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1afdec
    0 references
    Whittaker confluent hypergeometric function
    Defining formula
    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.m2agdec
    0 references
     
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