Gauss Multiplication Formula

Author

Eric W. Weisstein
September 6, 2008

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

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

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

Formula

(∏_(k=0)^(n-1))Γ((k/n)+z)==(((2 π))^((n-1)/2)) (n^((1/2)-n z))Γ(n z)

FullSimplify[Subtract@@@Table[{Product[Gamma[z+(k/n)],{k,0,n-1}],(((2π))^((n-1)/2))(n^(1/2-n z))Gamma[n z]},{n,10}]]

V6

Product[Gamma[z+(k/n)],{k,0,n-1}]

V7

Product[Gamma[z+(k/n)],{k,0,n-1}]