DLMF:13.15.E19 (Q4544): 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.m1addec

Revision as of 15:09, 2 January 2020

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DLMF:13.15.E19
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    Statements

    test
    d n d z n ⁡ ( e - 1 2 ⁢ z ⁢ z - μ - 1 2 ⁢ M κ , μ ⁡ ( z ) ) = ( - 1 ) n ⁢ ( 1 2 + μ + κ ) n ( 1 + 2 ⁢ μ ) n ⁢ e - 1 2 ⁢ z ⁢ z - μ - 1 2 ⁢ ( n + 1 ) ⁢ M 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-M 𝜅 𝜇 𝑧 superscript 1 𝑛 Pochhammer 1 2 𝜇 𝜅 𝑛 Pochhammer 1 2 𝜇 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜇 1 2 𝑛 1 Whittaker-confluent-hypergeometric-M 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}}M_{\kappa,\mu}\left(z\right)\right)=(-1)^{n% }\frac{{\left(\frac{1}{2}+\mu+\kappa\right)_{n}}}{{\left(1+2\mu\right)_{n}}}e^% {-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\*M_{\kappa+\frac{1}{2}n,\mu+\frac{1}{% 2}n}\left(z\right),}}
    0 references
    DLMF id
    DLMF:13.15.E19
    0 references
    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1addec
    0 references
     
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