DLMF:5.8.E3 (Q2087): Difference between revisions

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Property / constraint
 

x 0 , - 1 , 𝑥 0 1 {\displaystyle{\displaystyle x\neq 0,-1,\dots}}

x\neq 0,-1,\dots
Property / constraint: x 0 , - 1 , 𝑥 0 1 {\displaystyle{\displaystyle x\neq 0,-1,\dots}} / rank
 
Normal rank

Revision as of 16:04, 30 December 2019

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DLMF:5.8.E3
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    Statements

    | Γ ( x ) Γ ( x + i y ) | 2 = k = 0 ( 1 + y 2 ( x + k ) 2 ) , superscript Euler-Gamma 𝑥 Euler-Gamma 𝑥 imaginary-unit 𝑦 2 superscript subscript product 𝑘 0 1 superscript 𝑦 2 superscript 𝑥 𝑘 2 {\displaystyle{\displaystyle\left|\frac{\Gamma\left(x\right)}{\Gamma\left(x+% \mathrm{i}y\right)}\right|^{2}=\prod_{k=0}^{\infty}\left(1+\frac{y^{2}}{(x+k)^% {2}}\right),}}
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    x 0 , - 1 , 𝑥 0 1 {\displaystyle{\displaystyle x\neq 0,-1,\dots}}
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