Definition:Hypergeometric Series

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

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


 * $\dfrac {\beta_{n + 1} } {\beta_n} = \dfrac {\map A n} {\map B n}$

where $\map A n$ and $\map B n$ are polynomials in $n$.