The integral representation of ![ln[Gamma(z)]](/images/equations/MalmstensFormula/Inline1.svg)
by
 |  |  |
(1)
|
 |  | )/tdt,](/images/equations/MalmstensFormula/Inline7.svg) |
(2)
|
where 
is the log gamma function and 
is the digamma function.
Malmstén's Formula
See also
Binet's Log Gamma Formulas, Gamma Function, Log Gamma FunctionExplore with Wolfram|Alpha
References
Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 1. New York: Krieger, pp. 20-21, 1981.Referenced on Wolfram|Alpha
Malmstén's FormulaCite this as:
Weisstein, Eric W. "Malmstén's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MalmstensFormula.html