About the Project
NIST

inverse function

AdvancedHelp

(0.008 seconds)

11—20 of 152 matching pages

11: 19.10 Relations to Other Functions
For relations to the Gudermannian function gd ( x ) and its inverse gd - 1 ( x ) 4.23(viii)), see (19.6.8) and
12: 4.15 Graphics
§4.15(i) Real Arguments
See accompanying text
Figure 4.15.7: Conformal mapping of sine and inverse sine. … Magnify
§4.15(iii) Complex Arguments: Surfaces
The corresponding surfaces for arccos ( x + i y ) , arccot ( x + i y ) , arcsec ( x + i y ) can be visualized from Figures 4.15.9, 4.15.11, 4.15.13 with the aid of equations (4.23.16)–(4.23.18).
13: 27.5 Inversion Formulas
§27.5 Inversion Formulas
27.5.2 d | n μ ( d ) = 1 n ,
27.5.3 g ( n ) = d | n f ( d ) f ( n ) = d | n g ( d ) μ ( n d ) .
14: 4.32 Inequalities
4.32.4 arctan x 1 2 π tanh x , x 0 .
15: 27.17 Other Applications
§27.17 Other Applications
16: 4.39 Continued Fractions
§4.39 Continued Fractions
4.39.2 arcsinh z 1 + z 2 = z 1 + 1 2 z 2 3 + 1 2 z 2 5 + 3 4 z 2 7 + 3 4 z 2 9 + ,
4.39.3 arctanh z = z 1 - z 2 3 - 4 z 2 5 - 9 z 2 7 - ,
For these and other continued fractions involving inverse hyperbolic functions see Lorentzen and Waadeland (1992, pp. 569–571). …
17: 8.18 Asymptotic Expansions of I x ( a , b )
Inverse Function
18: 8.12 Uniform Asymptotic Expansions for Large Parameter
Inverse Function
For asymptotic expansions, as a , of the inverse function x = x ( a , q ) that satisfies the equation …These expansions involve the inverse error function inverfc ( x ) 7.17), and are uniform with respect to q [ 0 , 1 ] . …
19: 4.24 Inverse Trigonometric Functions: Further Properties
§4.24 Inverse Trigonometric Functions: Further Properties
§4.24(i) Power Series
§4.24(ii) Derivatives
§4.24(iii) Addition Formulas
4.24.17 Arctan u ± Arccot v = Arctan ( u v ± 1 v u ) = Arccot ( v u u v ± 1 ) .
20: 4.38 Inverse Hyperbolic Functions: Further Properties
§4.38 Inverse Hyperbolic Functions: Further Properties
§4.38(i) Power Series
§4.38(ii) Derivatives
§4.38(iii) Addition Formulas
4.38.19 Arctanh u ± Arccoth v = Arctanh ( u v ± 1 v ± u ) = Arccoth ( v ± u u v ± 1 ) .