- In mathematics, the
Gudermannian function relates a
hyperbolic angle measure ψ {\textstyle \psi } to a
circular angle measure ϕ {\textstyle \phi } called...
-
September 1852) was a
German mathematician noted for
introducing the
Gudermannian function and the
concept of
uniform convergence, and for
being the teacher...
- )}\equiv \operatorname {gd} \psi .}
where gd(ψ) is the
Gudermannian function. The
Gudermannian function gives a
direct relationship between the circular...
- the
secant function starting from 0 {\displaystyle 0} is the
inverse Gudermannian function, gd − 1 . {\textstyle \operatorname {gd} ^{-1}.} For numerical...
-
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...
- ^{-1}\phi ,}
where gd−1{\textstyle \operatorname {gd} ^{-1}} is the
inverse Gudermannian function, and artanhx=12ln1+x1−x{\textstyle \operatorname {artanh}...
-
Dirichlet distribution, a
probability distribution used in
statistics Gudermannian function, used in map-making
Georgia Dome, a
stadium in Atlanta, Georgia...
- map tilenames". openstreetmap.org.
Retrieved 2018-11-14. See
Inverse Gudermannian_function: gd − 1 x = ln | tan ( x 2 + π 4 ) | {\displaystyle \operatorname...
- mapping, just as the
circular angle is
invariant under rotation. The
Gudermannian function gives a
direct relationship between the
circular functions and...
- {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...
