DLMF:13.26.E9 (Q4661): Difference between revisions

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‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11566 / rank
 
Normal rank
Property / Symbols used: Q11566 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11566 / qualifier
 
xml-id: C13.S1.XMD4.m1hdec

Revision as of 01:07, 2 January 2020

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DLMF:13.26.E9
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    Statements

    Defining formula
    e - 1 2 ⁢ y ⁢ ( x + y x ) κ ⁢ ∑ n = 0 ∞ ( 1 2 + μ - κ ) n ⁢ ( 1 2 - μ - κ ) n n ! ⁢ ( y x + y ) n ⁢ W κ - n , μ ⁡ ( x ) , superscript 𝑒 1 2 𝑦 superscript 𝑥 𝑦 𝑥 𝜅 superscript subscript 𝑛 0 Pochhammer 1 2 𝜇 𝜅 𝑛 Pochhammer 1 2 𝜇 𝜅 𝑛 𝑛 superscript 𝑦 𝑥 𝑦 𝑛 Whittaker-confluent-hypergeometric-W 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}}{% \left(\frac{1}{2}-\mu-\kappa\right)_{n}}}{n!}\*\left(\frac{y}{x+y}\right)^{n}W% _{\kappa-n,\mu}\left(x\right),}}
    0 references
    DLMF id
    DLMF:13.26.E9
    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.m1ahdec
    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.m2abdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5ahdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1hdec
    0 references
    Q11566
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1hdec
    0 references
     
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