Definition:Hypergeometric Series

Definition
A hypergeometric series is a power series:
 * $\beta_0 + \beta_1 z + \beta_2 z^2 + \dots = \sum_{n \ge 0} \beta_n z^n$

in which the ratio of successive coefficients is a rational function of $n$:


 * $\dfrac {\beta_{n+1} } {\beta_n} = \dfrac {A \left({n}\right)} {B \left({n}\right)}$

where $A \left({n}\right)$ and $B \left({n}\right)$ are polynomials in $n$.