Formula:KLS:01.02:01

<< Orthogonal polynomials

formula in The gamma and beta function

Formula:KLS:01.02:02 >>

${\displaystyle{\displaystyle{\displaystyle{}\Gamma\left(z\right):=\int_{0}^{\infty}t^{z-1}{\mathrm{e}^{-t}}\,dt}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\Re{z}>0}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : 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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<< Orthogonal polynomials

formula in The gamma and beta function

Formula:KLS:01.02:02 >>