Hypergeometric 2F1

The (Gauss) hypergeometric ${}_2F_1$ function (often written simply as $F$) is defined by the series $${}_2F_1(a,b;c;z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(a)_k (b)_k}{(c)_k} \dfrac{z^k}{k!},$$ where $(a)_k$ denotes the Pochhammer symbol.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... [[Limit of (1/Gamma(c))*2F1(a,b;c;z) as c->-m|(next)]]: 15.1.1