DLMF:5.9.E3 (Q2092): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2abdec

Revision as of 18:35, 1 January 2020

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DLMF:5.9.E3
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    Statements

    test
    c - z ⁢ Γ ⁡ ( z ) = ∫ - ∞ ∞ | t | 2 ⁢ z - 1 ⁢ e - c ⁢ t 2 ⁢ d t , superscript 𝑐 𝑧 Euler-Gamma 𝑧 superscript subscript superscript 𝑡 2 𝑧 1 superscript 𝑒 𝑐 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle c^{-z}\Gamma\left(z\right)=\int_{-\infty}^{\infty% }|t|^{2z-1}e^{-ct^{2}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:5.9.E3
    0 references
    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
    0 references
    c > 0 𝑐 0 {\displaystyle{\displaystyle c>0}}
    0 references
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
     
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