Formula:KLS:01.02:08

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formula in The gamma and beta function

Formula:KLS:01.02:09 >>

${\displaystyle{\displaystyle{\displaystyle\Gamma\left(x+\mathrm{i}y\right)\sim\sqrt{2\pi}\,|y|^{x-1/2}{\mathrm{e}^{-|y|\pi/2}}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle|y|\rightarrow\infty}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle\tilde{}}}}$ : 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

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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