Clausen's Product Identity

Download Wolfram Notebook

Clausen's product identity is given by

_2F_1(1/4+a,1/4+b;1+a+b;z)_2F_1(1/4-a,1/4-b;1-a-b;z)
=_3F_2(1/2,1/2+a-b,1/2-a+b;1+a+b,1-a-b;z),

where is a hypergeometric function and is a generalized hypergeometric function.

Explore with Wolfram|Alpha

More things to try:

clausen's product identity
asymptotes x^2 + y^3 = (x y)^2
foci of hyperbola with semiaxes 3,4

References

Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 118, 1998.

Referenced on Wolfram|Alpha

Clausen's Product Identity

Cite this as:

Weisstein, Eric W. "Clausen's Product Identity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ClausensProductIdentity.html

Clausen's Product Identity

Explore with Wolfram|Alpha

References

Referenced on Wolfram|Alpha

Cite this as:

Subject classifications