# §4.1 Special Notation

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

 integers. real or complex constants. real variables. complex variable. base of natural logarithms.

It is assumed the user is familiar with the definitions and properties of elementary functions of real arguments . The main purpose of the present chapter is to extend these definitions and properties to complex arguments .

The main functions treated in this chapter are the logarithm , ; the exponential , ; the circular trigonometric (or just trigonometric) functions , , , , , ; the inverse trigonometric functions , , etc.; the hyperbolic trigonometric (or just hyperbolic) functions , , , , , ; the inverse hyperbolic functions , , etc.

Sometimes in the literature the meanings of and are interchanged; similarly for and , etc. Sometimes “arc” is replaced by the index “−1”, e.g. for and for .