# inverse

(0.001 seconds)

## 1—10 of 157 matching pages

##### 3: 22.15 Inverse Functions
###### §22.15(i) Definitions
Each of these inverse functions is multivalued. The principal values satisfy …
##### 4: 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).
##### 5: 4.47 Approximations
###### §4.47(i) Chebyshev-Series Expansions
Clenshaw (1962) and Luke (1975, Chapter 3) give 20D coefficients for $\ln$, $\exp$, $\sin$, $\cos$, $\tan$, $\cot$, $\operatorname{arcsin}$, $\operatorname{arctan}$, $\operatorname{arcsinh}$. … Hart et al. (1968) give $\ln$, $\exp$, $\sin$, $\cos$, $\tan$, $\cot$, $\operatorname{arcsin}$, $\operatorname{arccos}$, $\operatorname{arctan}$, $\sinh$, $\cosh$, $\tanh$, $\operatorname{arcsinh}$, $\operatorname{arccosh}$. … Luke (1975, Chapter 3) supplies real and complex approximations for $\ln$, $\exp$, $\sin$, $\cos$, $\tan$, $\operatorname{arctan}$, $\operatorname{arcsinh}$. …
##### 6: 4.29 Graphics
###### §4.29(i) Real Arguments Figure 4.29.2: Principal values of arcsinh ⁡ x and arccosh ⁡ x . … Magnify Figure 4.29.4: Principal values of arctanh ⁡ x and arccoth ⁡ 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. …
##### 7: 4.1 Special Notation
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. Sometimes in the literature the meanings of $\ln$ and $\operatorname{Ln}$ are interchanged; similarly for $\operatorname{arcsin}z$ and $\operatorname{Arcsin}z$, etc. …${\sin^{-1}}z$ for $\operatorname{arcsin}z$ and $\mathrm{Sin}^{-1}\;z$ for $\operatorname{Arcsin}z$.
##### 8: 7.17 Inverse Error Functions
###### §7.17(i) Notation
The inverses of the functions $x=\operatorname{erf}y$, $x=\operatorname{erfc}y$, $y\in\mathbb{R}$, are denoted by …
##### 9: 4.24 Inverse Trigonometric Functions: Further Properties
###### §4.24(ii) Derivatives
4.24.17 $\operatorname{Arctan}u\pm\operatorname{Arccot}v=\operatorname{Arctan}\left(% \frac{uv\pm 1}{v\mp u}\right)=\operatorname{Arccot}\left(\frac{v\mp u}{uv\pm 1% }\right).$
4.38.19 $\operatorname{Arctanh}u\pm\operatorname{Arccoth}v=\operatorname{Arctanh}\left(% \frac{uv\pm 1}{v\pm u}\right)=\operatorname{Arccoth}\left(\frac{v\pm u}{uv\pm 1% }\right).$