DLMF:10.17.E16 (Q3185): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: rescaled terminant function / rank
 
Normal rank
Property / Symbols used: rescaled terminant function / qualifier
 
test:

G p ⁡ ( z ) rescaled-terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle G_{\NVar{p}}\left(\NVar{z}\right)}}

\scterminant{\NVar{p}}@{\NVar{z}}
Property / Symbols used: rescaled terminant function / qualifier
 
xml-id: C9.S7.E22.m2adec

Revision as of 14:32, 2 January 2020

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DLMF:10.17.E16
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    Statements

    test
    G p ⁡ ( z ) = e z 2 ⁢ π ⁢ Γ ⁡ ( p ) ⁢ Γ ⁡ ( 1 - p , z ) , rescaled-terminant-function 𝑝 𝑧 superscript 𝑒 𝑧 2 𝜋 Euler-Gamma 𝑝 incomplete-Gamma 1 𝑝 𝑧 {\displaystyle{\displaystyle G_{p}\left(z\right)=\frac{e^{z}}{2\pi}\Gamma\left% (p\right)\Gamma\left(1-p,z\right),}}
    0 references
    DLMF id
    DLMF:10.17.E16
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    incomplete gamma function
    test
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2adec
    0 references
    rescaled terminant function
    test
    G p ⁡ ( z ) rescaled-terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle G_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C9.S7.E22.m2adec
    0 references
     
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