…
►are denoted respectively by
…Each of these inversefunctions is multivalued.
…and unless stated otherwise it is assumed that the inversefunctions assume their principal values.
…
►For representations of the inversefunctions as symmetric elliptic integrals see §19.25(v).
…
…
►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.
…
►For sums of trigonometric and inverse trigonometric functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §§14–42), Oberhettinger (1973), and Prudnikov et al. (1986a, Chapter 5).
…
►►►Figure 4.29.6: Principal values of and .
…
Magnify►
§4.29(ii) Complex Arguments
…
►The surfaces for the complex hyperbolic and inverse hyperbolic functions are similar to the surfaces depicted in §4.15(iii) for the trigonometric and inverse trigonometric functions.
…