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DLMF:8.18.E13
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Formula:3379
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MaRDI QID
Q3379
Label: DLMF:8.18.E13
Digital Library of Mathematical Functions ID
8.18.E13
Γ
~
(
z
)
=
(
2
π
)
-
1
/
2
e
z
z
(
1
/
2
)
-
z
Γ
(
z
)
,
~
Γ
𝑧
superscript
2
𝜋
1
2
superscript
𝑒
𝑧
superscript
𝑧
1
2
𝑧
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\widetilde{\Gamma}(z)=(2\pi)^{-1/2}e^{z}z^{(1/2)-z% }\Gamma\left(z\right),}}
Constraint(s)
Symbols List
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
: gamma function
π
{\displaystyle{\displaystyle\pi}}
: the ratio of the circumference of a circle to its diameter
e
{\displaystyle{\displaystyle\mathrm{e}}}
: base of natural logarithm
z
𝑧
{\displaystyle{\displaystyle z}}
: complex variable
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