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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(iv) Logarithmic Forms
Other Inverse Functions
2: 4.23 Inverse Trigonometric Functions
§4.23 Inverse Trigonometric Functions
§4.23(i) General Definitions
Other Inverse Functions
§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
§7.17(i) Notation
y = inverf x ,
y = inverfc x ,
§7.17(ii) Power Series
§7.17(iii) Asymptotic Expansion of inverfc x for Small x
5: 4.1 Special Notation
k , m , n integers.
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 , Ln z ; the exponential exp z , 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 , Arcsin z , etc. ; the hyperbolic trigonometric (or just hyperbolic) functions sinh z , cosh z , tanh z , csch z , sech z , coth z ; the inverse hyperbolic functions arcsinh z , Arcsinh z , etc. …
6: 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).
7: 4.46 Tables
§4.46 Tables
8: 7.22 Methods of Computation
§7.22(i) Main Functions
9: 4.47 Approximations
§4.47 Approximations
§4.47(i) Chebyshev-Series Expansions
10: 4.29 Graphics
§4.29(i) Real Arguments
See accompanying text
Figure 4.29.6: Principal values of arccsch x and arcsech x . … Magnify
§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. …