hyperbolic functions
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1: 4.37 Inverse Hyperbolic Functions
§4.37 Inverse Hyperbolic Functions
►§4.37(i) General Definitions
… ►§4.37(ii) Principal Values
… ► … ►§4.37(vi) Interrelations
…2: 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 .
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►; the hyperbolic trigonometric (or just hyperbolic) functions
, , , , , ; the inverse hyperbolic functions
, , etc.
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integers. | |
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3: 4.41 Sums
§4.41 Sums
►For sums of hyperbolic functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §43), Prudnikov et al. (1986a, §5.3), and Zucker (1979).4: 4.28 Definitions and Periodicity
§4.28 Definitions and Periodicity
… ►Relations to Trigonometric Functions
… ►As a consequence, many properties of the hyperbolic functions follow immediately from the corresponding properties of the trigonometric functions. ►Periodicity and Zeros
►The functions and have period , and has period . …5: 4.29 Graphics
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§4.29(i) Real Arguments
… ► ►§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. …6: 4.31 Special Values and Limits
7: 4.46 Tables
§4.46 Tables
…8: 4.32 Inequalities
§4.32 Inequalities
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4.32.1
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4.32.2
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4.32.3
, ,
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►For these and other inequalities involving hyperbolic functions see Mitrinović (1964, pp. 61, 76, 159) and Mitrinović (1970, p. 270).