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Malmstén's Formula

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The integral representation of ln[Gamma(z)] by

lnGamma(z)=int_1^zpsi_0(z^')dz^'
(1)
=int_0^infty[(z-1)-(1-e^(-(z-1)t))/(1-e^(-t))](e^(-t))/tdt,
(2)

where lnGamma(z) is the log gamma function and psi_0(z) is the digamma function.

See also

Binet's Log Gamma Formulas, Gamma Function, Log Gamma Function

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References

Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 1. New York: Krieger, pp. 20-21, 1981.

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Malmstén's Formula

Cite this as:

Weisstein, Eric W. "Malmstén's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MalmstensFormula.html

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