# §5.1 Special Notation

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

 nonnegative integers. nonnegative integer, except in §5.20. real variables. complex variable. real or complex variables with . arbitrary small positive constant. Euler’s constant (§5.2(ii)). derivatives with respect to the variable.

The main functions treated in this chapter are the gamma function , the psi function (or digamma function) , the beta function , and the -gamma function .

The notation is due to Legendre. Alternative notations for this function are: (Gauss) and . Alternative notations for the psi function are: (Gauss) Jahnke and Emde (1945); Davis (1933); Pairman (1919).