Hypergeometric 3F2

The hypergeometric function ${}_3F_2$ is defined by $${}_3F_2(a_1,a_2,a_3; b_1,b_2; z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1)_k(a_2)_k(a_3)_k}{(b_1)_k(b_2)_k(b_3)_k} \dfrac{z^k}{k!},$$ where $(a)_k$ denotes the Pochhammer symbol.

Properties

2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)

References

Hypergeometric functions

Hypergeometric ${}_pF_q$

Hypergeometric 0F0

Hypergeometric 1F0

Hypergeometric 0F1

Hypergeometric 2F1