A Hypergeometric Function in which one parameter changes by +1 or is said to be contiguous. There are 26 functions contiguous to 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
Abramowitz, M. and Stegun, C. A. (Eds.).
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, 1972.