About the Project

inverse Gudermannian function

AdvancedHelp

(0.003 seconds)

8 matching pages

1: 19.6 Special Cases
For the inverse Gudermannian function gd 1 ( ϕ ) see §4.23(viii). …
2: 4.23 Inverse Trigonometric Functions
The inverse Gudermannian function is given by
4.23.41 gd 1 ( x ) = 0 x sec t d t , 1 2 π < x < 1 2 π .
3: 4.46 Tables
§4.46 Tables
4: 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
5: 4.26 Integrals
4.26.5 sec x d x = gd 1 ( x ) , 1 2 π < x < 1 2 π .
6: 19.9 Inequalities
7: 22.16 Related Functions
§22.16(i) Jacobi’s Amplitude ( am ) Function
where the inverse sine has its principal value when K x K and is defined by continuity elsewhere. … For the Gudermannian function gd ( x ) see §4.23(viii). …
§22.16(ii) Jacobi’s Epsilon Function
§22.16(iii) Jacobi’s Zeta Function
8: 4.40 Integrals
§4.40 Integrals
§4.40(ii) Indefinite Integrals
§4.40(iii) Definite Integrals
§4.40(iv) Inverse Hyperbolic Functions
Extensive compendia of indefinite and definite integrals of hyperbolic functions include Apelblat (1983, pp. 96–109), Bierens de Haan (1939), Gröbner and Hofreiter (1949, pp. 139–160), Gröbner and Hofreiter (1950, pp. 160–167), Gradshteyn and Ryzhik (2000, Chapters 2–4), and Prudnikov et al. (1986a, §§1.4, 1.8, 2.4, 2.8).