►For sums of trigonometric and inverse trigonometric functions see Gradshteyn and Ryzhik (2015, Chapter 1), Hansen (1975, §§14–42), Oberhettinger (1973), and Prudnikov et al. (1986a, Chapter 5).
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►►►Figure 4.29.2: Principal values of and .
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Magnify
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►►►Figure 4.29.4: Principal values of and .
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Magnify
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§4.29(ii) Complex Arguments
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►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.
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►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.
… for and for .