Definition of Gudermannian. Meaning of Gudermannian. Synonyms of Gudermannian

- In mathematics, the Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called...
- Arctangent function f ( x ) = arctan ⁡ x {\displaystyle f(x)=\arctan x} Gudermannian function f ( x ) = gd ⁡ ( x ) = ∫ 0 x d t cosh ⁡ t = 2 arctan ⁡ ( tanh...
- the secant function starting from 0 {\displaystyle 0} is the inverse Gudermannian function, gd − 1 . {\textstyle \operatorname {gd} ^{-1}.} For numerical...
- )}\equiv \operatorname {gd} \psi .} where gd(ψ) is the Gudermannian function. The Gudermannian function gives a direct relationship between the circular...
- September 1852) was a German mathematician noted for introducing the Gudermannian function and the concept of uniform convergence, and for being the teacher...
- {\displaystyle \textstyle \operatorname {gd} ^{-1}} ⁠ is the inverse Gudermannian function. Ideal points (points at infinity) in the Poincaré half-plane...
- map tilenames". openstreetmap.org. Retrieved 2018-11-14. See Inverse Gudermannian_function: gd − 1 ⁡ x = ln ⁡ | tan ⁡ ( x 2 + π 4 ) | {\displaystyle \operatorname...
- {x-c}{a}}\right|^{2b}}}} Hyperbolic secant. This is also the derivative of the Gudermannian function. f ( x ) = sech ⁡ ( x ) = 2 e x + e − x {\displaystyle f(x)=\operatorname...
- mapping, just as the circular angle is invariant under rotation. The Gudermannian function gives a direct relationship between the circular functions and...
- sinh ⁡ v {\displaystyle \operatorname {gd} v=\arctan \sinh v} is the Gudermannian function. Several other curves can be derived from the hyperbola by inversion...