Malmstén's Formula

Author

Eric W. Weisstein
November 23, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/MalmstensFormula.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MalmstensFormula.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Integrals

(∫_1^z)(PolyGamma[z])dz==(LogGamma[z])

Integrate[PolyGamma[z],{z,1,z}]

(∫_0^∞)((exp(-t))/t) ((z-1)-((1-exp(t (-(z-1))))/(1-exp(-t))))dt==(LogGamma[z])

V7

Integrate[((z-1)-((1-Exp[-(z-1)t])/(1-Exp[-t])))((Exp[-t])/t),{t,0,∞}]

With[{z=1.1+2I},NIntegrate[((z-1)-((1-Exp[-(z-1)t])/(1-Exp[-t])))((Exp[-t])/t),{t,0,∞}]]

LogGamma[1.1+2I]