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1: 4.37 Inverse Hyperbolic Functions

§4.37 Inverse Hyperbolic Functions

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§4.37(i) General Definitions

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§4.37(ii) Principal Values

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§4.37(iv) Logarithmic Forms

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Other Inverse Functions

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2: 4.23 Inverse Trigonometric Functions

§4.23 Inverse Trigonometric Functions

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§4.23(i) General Definitions

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Other Inverse Functions

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§4.23(vii) Special Values and Interrelations

… ►The inverse Gudermannian function is given by …

3: 22.15 Inverse Functions

§22.15 Inverse Functions

… ►are denoted respectively by …Each of these inverse functions is multivalued. …and unless stated otherwise it is assumed that the inverse functions assume their principal values. … ►For representations of the inverse functions as symmetric elliptic integrals see §19.25(v). …

4: 7.17 Inverse Error Functions

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§7.17(i) Notation

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$y=\mathrm{inverf}x,$

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$y=\mathrm{inverfc}x,$

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§7.17(ii) Power Series

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§7.17(iii) Asymptotic Expansion of $\mathrm{inverfc}x$ for Small $x$

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5: 4.1 Special Notation

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$k,m,n$	integers.
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… ►The main purpose of the present chapter is to extend these definitions and properties to complex arguments $z$. ►The main functions treated in this chapter are the logarithm $\ln z$, $\mathrm{Ln}z$; the exponential $\exp z$, ${\mathrm{e}}^z$; the circular trigonometric (or just trigonometric) functions $\sin z$, $\cos z$, $\tan z$, $\csc z$, $\sec z$, $\cot z$; the inverse trigonometric functions $\arcsin z$, $\mathrm{Arcsin}z$, etc. ; the hyperbolic trigonometric (or just hyperbolic) functions $\sinh z$, $\cosh z$, $\tanh z$, $\mathrm{csch}z$, $\mathrm{sech}z$, $\coth z$; the inverse hyperbolic functions $\mathrm{arcsinh}z$, $\mathrm{Arcsinh}z$, etc. …

6: 4.27 Sums

§4.27 Sums

►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).

7: 4.46 Tables

§4.46 Tables

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8: 7.22 Methods of Computation

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§7.22(i) Main Functions

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9: 4.47 Approximations

§4.47 Approximations

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§4.47(i) Chebyshev-Series Expansions

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10: 4.29 Graphics

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§4.29(i) Real Arguments

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Figure 4.29.6: Principal values of $\mathrm{arccsch}x$ and $\mathrm{arcsech}x$. … Magnify

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§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. …