[Calculation 1] Fundamentals of Hypergeometric Functions

Hypergeometric Functions

The classical hypergeometric function ${}_{2}F_1$ is defined by $$ {}_{2}F_1(a,b;c;z) = \sum_{k=0}^\infty \frac{(a)_k(b)_k}{(c)_k} \frac{z^k}{k!} $$ where $(\cdot)_k$ is Pochhammer symbol, that is, $$ (q)_k = \frac{\Gamma(q+k)}{\Gamma(q)} $$ provided that $q+k$ is not a negative integer, with the convention $1/{\pm\infty} = … Continue reading