# §16.3 Derivatives and Contiguous Functions

## §16.3(i) Differentiation Formulas

16.3.1
16.3.2
16.3.3
16.3.4

Other versions of these identities can be constructed with the aid of the operator identity

16.3.5.

## §16.3(ii) Contiguous Functions

Two generalized hypergeometric functions are (generalized) contiguous if they have the same pair of values of and , and corresponding parameters differ by integers. If , then any distinct contiguous functions are linearly related. Examples are provided by the following recurrence relations:

For further examples see §§13.3(i), 15.5(ii), and the following references: Rainville (1960, §48), Wimp (1968), and Luke (1975, §5.13).