Clausen's Product Identity

Author

Eric W. Weisstein
April 22, 2004

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

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Numerical Check

Subtract@@@Table[{Hypergeometric2F1[(1/4)+a,(1/4)+b,1+a+b,x]Hypergeometric2F1[(1/4)-a,(1/4)-b,1-a-b,x],HypergeometricPFQ[{(1/2),(1/2)+a-b,(1/2)-a+b},{1+a+b,1-a-b},x]}/.{a->Random[Complex,(I+1){-1,1},20],b->Random[Complex,(I+1){-1,1},20],x->Random[Complex,(I+1){-1,1},20]},{100}]//Chop//Union