Formula:KLS:01.02:09

<< Formula:KLS:01.02:08

formula in The gamma and beta function

Formula:KLS:01.02:10 >>

${\displaystyle{\displaystyle{\displaystyle\frac{\Gamma\left(z+a\right)}{\Gamma\left(z+b\right)}\sim z^{a-b},\quad a,b\in\mathbb{C}}}}$

Constraint(s)

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

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
${\displaystyle{\displaystyle{\displaystyle\in}}}$ : element of : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r9

Bibliography

Equation in Section 1.2 of KLS.

URL links

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<< Formula:KLS:01.02:08

formula in The gamma and beta function

Formula:KLS:01.02:10 >>