DLMF:8.5.E5 (Q2514): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1ddec

Latest revision as of 13:41, 2 January 2020

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DLMF:8.5.E5
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    Statements

    Defining formula
    Γ ⁡ ( a , z ) = e - 1 2 ⁢ z ⁢ z 1 2 ⁢ a - 1 2 ⁢ W 1 2 ⁢ a - 1 2 , 1 2 ⁢ a ⁡ ( z ) . incomplete-Gamma 𝑎 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 1 2 𝑎 1 2 Whittaker-confluent-hypergeometric-W 1 2 𝑎 1 2 1 2 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=e^{-\frac{1}{2}z}z^{\frac{1% }{2}a-\frac{1}{2}}W_{\frac{1}{2}a-\frac{1}{2},\frac{1}{2}a}\left(z\right).}}
    0 references
    DLMF id
    DLMF:8.5.E5
    0 references
    Symbols used
    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.m2addec
    0 references
    incomplete gamma function
    Defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2aadec
    0 references
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1ddec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1ddec
    0 references
     
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