# §14.1 Special Notation

(For other notation see Notation for the Special Functions.)

 , , real variables. complex variable. nonnegative integers used for order and degree, respectively. general order and degree, respectively. complex degree, . Euler’s constant (§5.2(ii)). arbitrary small positive constant. logarithmic derivative of gamma function (§5.2(i)). . Olver’s scaled hypergeometric function: .

Multivalued functions take their principal values (§4.2(i)) unless indicated otherwise.

The main functions treated in this chapter are the Legendre functions , , , ; Ferrers functions , (also known as the Legendre functions on the cut); associated Legendre functions , , ; conical functions , , , , (also known as Mehler functions).

Among other notations commonly used in the literature Erdélyi et al. (1953a) and Olver (1997b) denote and by and , respectively. Magnus et al. (1966) denotes , , , and by , , , and , respectively. Hobson (1931) denotes both and by ; similarly for and .