inverse trigonometric functions
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1: 4.23 Inverse Trigonometric Functions
§4.23 Inverse Trigonometric Functions
►§4.23(i) General Definitions
… ► … ►§4.23(iv) Logarithmic Forms
… ►§4.23(vii) Special Values and Interrelations
…2: 4.27 Sums
§4.27 Sums
►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).3: 4.1 Special Notation
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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.
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integers. | |
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4: 19.10 Relations to Other Functions
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19.10.2
5: 4.29 Graphics
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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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6: 4.46 Tables
§4.46 Tables
…7: 4.47 Approximations
8: 4.37 Inverse Hyperbolic Functions
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4.37.4
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►Each is two-valued on the corresponding cut(s), and each is real on the part of the real axis that remains after deleting the intersections with the corresponding cuts.
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4.37.7
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4.37.8
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4.37.9
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9: 4.15 Graphics
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§4.15(i) Real Arguments
… ► ►§4.15(iii) Complex Arguments: Surfaces
… ►The corresponding surfaces for , , can be visualized from Figures 4.15.9, 4.15.11, 4.15.13 with the aid of equations (4.23.16)–(4.23.18).10: 4.32 Inequalities
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4.32.4
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