# for inverse function

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##### 2: 4.23 Inverse Trigonometric Functions
###### §4.23(vii) Special Values and Interrelations
The inverse Gudermannian function is given by …
##### 3: 22.15 Inverse Functions
###### §22.15 InverseFunctions
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
$y=\operatorname{inverf}x,$
$y=\operatorname{inverfc}x,$
##### 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 $\ln z$, $\operatorname{Ln}z$; 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 $\operatorname{arcsin}z$, $\operatorname{Arcsin}z$, etc. ; the hyperbolic trigonometric (or just hyperbolic) functions $\sinh z$, $\cosh z$, $\tanh z$, $\operatorname{csch}z$, $\operatorname{sech}z$, $\coth z$; the inverse hyperbolic functions $\operatorname{arcsinh}z$, $\operatorname{Arcsinh}z$, 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).
##### 10: 4.29 Graphics
###### §4.29(i) Real Arguments 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. …