DLMF:13.26.E3 (Q4655): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
Defining formula:

( 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.m1abdec

Revision as of 01:06, 2 January 2020

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DLMF:13.26.E3
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    Statements

    Defining formula
    e - 1 2 ⁢ y ⁢ ( x + y x ) κ ⁢ ∑ n = 0 ∞ ( 1 2 + μ - κ ) n ⁢ y n n ! ⁢ ( x + y ) n ⁢ M κ - n , μ ⁡ ( x ) , superscript 𝑒 1 2 𝑦 superscript 𝑥 𝑦 𝑥 𝜅 superscript subscript 𝑛 0 Pochhammer 1 2 𝜇 𝜅 𝑛 superscript 𝑦 𝑛 𝑛 superscript 𝑥 𝑦 𝑛 Whittaker-confluent-hypergeometric-M 𝜅 𝑛 𝜇 𝑥 {\displaystyle{\displaystyle e^{-\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{% \kappa}\sum_{n=0}^{\infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{n}}y^{n}% }{n!(x+y)^{n}}M_{\kappa-n,\mu}\left(x\right),}}
    0 references
    DLMF id
    DLMF:13.26.E3
    0 references
    constraint
    ℜ ⁡ ( y / x ) > - 1 2 𝑦 𝑥 1 2 {\displaystyle{\displaystyle\Re(y/x)>-\frac{1}{2}}}
    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.m1abdec
    0 references
     
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