Contiguous Function

A Hypergeometric Function in which one parameter changes by +1 or $-1$ is said to be contiguous. There are 26 functions contiguous to ${}_2F_1(a,b;c;x)$ taking one pair at a time. There are 325 taking two or more pairs at a time. See Abramowitz and Stegun (1972, pp. 557-558).

See also Hypergeometric Function

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.