- In mathematics, the
Gudermannian function relates a
hyperbolic angle measure ψ {\textstyle \psi } to a
circular angle measure ϕ {\textstyle \phi } called...
- )}\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...
-
September 1852) was a
German mathematician noted for
introducing the
Gudermannian function and the
concept of
uniform convergence, and for
being the teacher...
- mapping, just as the
circular angle is
invariant under rotation. The
Gudermannian function gives a
direct relationship between the
circular functions and...
- (}{\tfrac {1}{2}}\pi +x{\bigr )}}} (the
integral of sec, the
inverse Gudermannian function),
arcsec ( 2 e x ) , {\textstyle \operatorname {arcsec} {\bigl...
- )-e\tanh ^{-1}(e\sin \phi )\right]\end{aligned}}}
where gd(x) is the
Gudermannian function. (See also
Mercator projection.) The
conformal latitude defines...
-
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...
