(For other notation see Notation for the Special Functions.)
integers. |
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real or complex constants. |
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real variables. |
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complex variable. |
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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 “”, e.g. for and for .