# §15.5 Derivatives and Contiguous Functions

## §15.5(i) Differentiation Formulas

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).

## §15.5(ii) Contiguous Functions

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 .