Formula:KLS:01.02:07

<< Formula:KLS:01.02:06

formula in The gamma and beta function

Formula:KLS:01.02:08 >>

${\displaystyle{\displaystyle{\displaystyle\Gamma\left(z\right)\sim\sqrt{2\cpi}\,z^{z-1/2}\expe^{-z}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\realpart{z}\rightarrow\infty}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
${\displaystyle{\displaystyle{\displaystyle\tilde{}}}}$ : asymptotic equality : http://dlmf.nist.gov/2.1#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle\Re{z}}}}$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation in Section 1.2 of KLS.

URL links

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formula in The gamma and beta function

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