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Gudermannian function

Index Gudermannian function

The Gudermannian function, named after Christoph Gudermann (1798–1852), relates the circular functions and hyperbolic functions without explicitly using complex numbers. [1]

20 relations: Angle of parallelism, Arthur Cayley, Casimir effect, Christoph Gudermann, Complex number, Crelle's Journal, Hyperbolic function, Hyperbolic geometry, Hyperbolic secant distribution, Integral of the secant function, Inverse hyperbolic functions, Inverse trigonometric functions, Inverted pendulum, Johann Heinrich Lambert, List of trigonometric identities, Mercator projection, Tangent half-angle formula, Tractrix, Transverse Mercator projection, Trigonometric functions.

Angle of parallelism

In hyperbolic geometry, the angle of parallelism \Pi(a), is the angle at one vertex of a right hyperbolic triangle that has two asymptotic parallel sides.

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Arthur Cayley

Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician.

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Casimir effect

In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field.

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Christoph Gudermann

Christoph Gudermann (March 25, 1798 – September 25, 1852) was a German mathematician noted for introducing the Gudermannian function and the concept of uniform convergence, and for being the teacher of Karl Weierstrass, who was greatly influenced by Gudermann's course on elliptic functions in 1839–1840, the first such course to be taught in any institute.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

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Hyperbolic function

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.

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Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

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Hyperbolic secant distribution

In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function.

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Integral of the secant function

The integral of the secant function of trigonometry was the subject of one of the "outstanding open problems of the mid-seventeenth century", solved in 1668 by James Gregory.

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Inverse hyperbolic functions

In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions.

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Inverse trigonometric functions

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).

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Inverted pendulum

An inverted pendulum is a pendulum that has its center of mass above its pivot point.

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Johann Heinrich Lambert

Johann Heinrich Lambert (Jean-Henri Lambert in French; 26 August 1728 – 25 September 1777) was a Swiss polymath who made important contributions to the subjects of mathematics, physics (particularly optics), philosophy, astronomy and map projections.

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List of trigonometric identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined.

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Mercator projection

The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569.

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Tangent half-angle formula

In trigonometry, tangent half-angle formulas relate the tangent of half of an angle to trigonometric functions of the entire angle.

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Tractrix

A tractrix (from the Latin verb trahere "pull, drag"; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a tractor (pulling) point that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed.

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Transverse Mercator projection

The transverse Mercator map projection is an adaptation of the standard Mercator projection.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Redirects here:

Gd(x), Gudermanian function, Gudermann function, Gudermannian, Transcendent angle.

References

[1] https://en.wikipedia.org/wiki/Gudermannian_function

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