Hypergeometric 2F3

The hypergeometric series ${}_2F_3$ is defined by the series $${}_2F_3(a_1,a_2;b_1,b_2,b_3;z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1)_k(a_2)_k}{(b_1)_k(b_2)_k(b_3)_k} \dfrac{z^k}{k!},$$ where $(a_1)_k$ denotes the Pochhammer symbol.

Properties

1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4)

References

Hypergeometric functions

Hypergeometric ${}_pF_q$

Hypergeometric 0F0

Hypergeometric 1F0

Hypergeometric 0F1

Hypergeometric 2F1