hyperbolic
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1: 4.37 Inverse Hyperbolic Functions
§4.37 Inverse Hyperbolic Functions
… ►The principal values of the inverse hyperbolic cosecant, hyperbolic secant, and hyperbolic tangent are given by … ►Inverse Hyperbolic Sine
… ►Inverse Hyperbolic Cosine
… ►Inverse Hyperbolic Tangent
…2: 36.2 Catastrophes and Canonical Integrals
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Normal Forms for Umbilic Catastrophes with Codimension
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36.2.3
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►(hyperbolic umbilic).
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Canonical Integrals
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36.2.27
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3: 4.35 Identities
§4.35 Identities
►§4.35(i) Addition Formulas
… ►§4.35(ii) Squares and Products
… ►§4.35(iii) Multiples of the Argument
… ►§4.35(iv) Real and Imaginary Parts; Moduli
…4: 4.29 Graphics
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§4.29(i) Real Arguments
… ► ►§4.29(ii) Complex Arguments
►The conformal mapping is obtainable from Figure 4.15.7 by rotating both the -plane and the -plane through an angle , compare (4.28.8). ►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. …5: 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 . …6: 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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7: 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).