Generalized hypergeometric function

Summary

The generalized hypergeometric function ${}_pF_q$ is a power series whose coefficient ratio is a rational function of $n$. That rational function has $p$ numerator parameters and $q$ denominator parameters. The hypergeometric function ${}_2F_1$ is the case $p = 2$, $q = 1$, and the exponential, the binomial series and the Bessel functions come from smaller $p$ and $q$. Many classical summation formulas, such as those of Pfaff–Saalschütz, Dixon and Dougall, are evaluations of ${}_3F_2$ and higher series at $z = 1$.