Other versions of several of the identities in this subsection can be constructed with the aid of the operator identity
See Erdélyi et al. (1953a, pp. 102–103).
The six functions , , are said to be contiguous to .
By repeated applications of (15.5.11)–(15.5.18) any function , in which are integers, can be expressed as a linear combination of and any one of its contiguous functions, with coefficients that are rational functions of , and .
An equivalent equation to the hypergeometric differential equation (15.10.1) is
Further contiguous relations include: