DLMF:13.15.E23 (Q4548): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1ahdec

Revision as of 15:09, 2 January 2020

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DLMF:13.15.E23
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    Statements

    test
    ( z ⁢ d d z ⁡ z ) n ⁢ ( e 1 2 ⁢ z ⁢ z - κ - 1 ⁢ W κ , μ ⁡ ( z ) ) = ( 1 2 + μ - κ ) n ⁢ ( 1 2 - μ - κ ) n ⁢ e 1 2 ⁢ z ⁢ z n - κ - 1 ⁢ W κ - n , μ ⁡ ( z ) , superscript 𝑧 derivative 𝑧 𝑧 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜅 1 Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 Pochhammer 1 2 𝜇 𝜅 𝑛 Pochhammer 1 2 𝜇 𝜅 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝑛 𝜅 1 Whittaker-confluent-hypergeometric-W 𝜅 𝑛 𝜇 𝑧 {\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(e^{\frac{1}{2}z}z^{-\kappa-1}W_{\kappa,\mu}\left(z\right)\right)={\left(% \tfrac{1}{2}+\mu-\kappa\right)_{n}}{\left(\tfrac{1}{2}-\mu-\kappa\right)_{n}}e% ^{\frac{1}{2}z}z^{n-\kappa-1}W_{\kappa-n,\mu}\left(z\right),}}
    0 references
    DLMF id
    DLMF:13.15.E23
    0 references
    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1ahdec
    0 references
     
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