DLMF:13.26.E7 (Q4659): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11580 / rank
 
Normal rank
Property / Symbols used: Q11580 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11580 / qualifier
 
xml-id: C13.S1.XMD5.m1fdec

Latest revision as of 01:07, 2 January 2020

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DLMF:13.26.E7
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    Statements

    Defining formula
    e - 1 2 ⁢ y ⁢ ( x x + y ) μ - 1 2 ⁢ ∑ n = 0 ∞ ( 1 2 - μ - κ ) n n ! ⁢ ( - y x ) n ⁢ W κ - 1 2 ⁢ n , μ - 1 2 ⁢ n ⁡ ( x ) , superscript 𝑒 1 2 𝑦 superscript 𝑥 𝑥 𝑦 𝜇 1 2 superscript subscript 𝑛 0 Pochhammer 1 2 𝜇 𝜅 𝑛 𝑛 superscript 𝑦 𝑥 𝑛 Whittaker-confluent-hypergeometric-W 𝜅 1 2 𝑛 𝜇 1 2 𝑛 𝑥 {\displaystyle{\displaystyle e^{-\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{\mu-% \frac{1}{2}}\sum_{n=0}^{\infty}\frac{{\left(\frac{1}{2}-\mu-\kappa\right)_{n}}% }{n!}\left(\frac{-y}{\sqrt{x}}\right)^{n}\*W_{\kappa-\frac{1}{2}n,\mu-\frac{1}% {2}n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:13.26.E7
    0 references
    constraint
    | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}
    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.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5afdec
    0 references
    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1fdec
    0 references
    Q11566
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1fdec
    0 references
    Q11580
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C13.S1.XMD5.m1fdec
    0 references
     
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