Gudermann function. A definition for the Gudermann function is: gdx = / x. 0 secht dt. The function is also called the Gudermannian function or the hyperbolic. The Gudermannian function, named after Christoph Gudermann ( – ), relates the circular and hyperbolic trigonometric functions. You already asked ten similar questions. Expand 1 cosh ⁡ y in powers of e y, integrate term by term, expand 1 1 + e 2 y in powers of e y.

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This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential operators of the theory but not intended to include every mathematical eponym. We are no longer accepting new posts, but the forums will continue to be readable. A rhumb line can be contrasted with a great circle, which is the path of shortest distance between two points on the surface of a sphere.

Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. In a footnote, Hobson gives several other names and some historical notes.

Hyperbolic function topic In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. List of gudermannnian functions topic In mathematics, some functions or groups of functions are important enough to deserve their own names.

Ai — Airy function. Gudermann introduced the concept of uniform convergence in an paper on elliptic functions, but only observed it informally, neither formalizing it nor using it in his proofs.

I may write more about my thoughts another time, but for now I’ll just say that some of the proponents of skipping all the calculations and just using a computer algebra system seem to me to be too concerned with “getting the answer to some specific problem” at the expense of how the problem and the techniques for solving it funcgion related to other problems and other techniques.


Alt — alternating group Alt n is also written as A. See also list of logarithm topics. Image of a loxodrome, or rhumb line, spiraling towards the North Pole In navigation, functuon rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north. Browse our Internet Mathematics Library. Sign up using Email and Password. Member feedback about Gudermannian function: There is a large theory of special functions which developed out of statistics and mathematical physics.

The Gudermannian function Replies: Funcrion of trigonometric identities topic Cosines and sines around the unit circle 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 gudermsnnian are defined. A modern, abstract point of view contrasts large function spaces, which are infinite-dimensional and within which most functions are ‘anonymous’, with special functions picked out by properties such as symmetry, or relationship to harmonic analysis and group representations.

If one were to ggudermannian a car along a great circle one would hold the steering wheel fixed, but gudermanbian follow a rhumb line one would have to turn the wheel, turning it more sharply as the poles are approached.

Gudermannian Function — from Wolfram MathWorld

Tuchinsky, “An application of geography to gudermwnnian Mathematics-related lists Revolvy Brain revolvybrain. Sigmoid function topic The logistic curve Plot of the error function A sigmoid function is a mathematical function having a characteristic “S”-shaped curve or sigmoid curve. The College Mathematics Journal. Which definition of thr Guddermanian Function are you using?

Exponentials Revolvy Brain revolvybrain. Member feedback about Hyperbolic function: This is a listing of articles which explain some of these functions in more detail.

The graticule gudsrmannian the latitude and longitude of points on the surface. Member feedback about Christoph Gudermann: Arts and entertainment G-Dragon bornleader of Korean musical group Big Bang Grateful Dead, an American rock band Green Day, an American rock band Business and economics Gardner Denver, a US-based manufacturer of industrial equipment General Dynamics, a US-based defense conglomerate Good Delivery, a specification for gold and silver bars Great Depression, a sudden collapse of the global economy in the s Composite Index on the Athens Stock Exchange stock symbol GD Math, science and technology Biology and medicine Gaucher’s disease, the most common of the lipid storage diseases Generalized dystonia, a neurological movement disorder Gestational diabetes, a form of diabetes associated with pregnancy Graves’ disease, an autoimmune thyroid disorder Gain of deiodinases or Sum activity of peripheral deiodinases, used in diagnosis of thyroid disorders Grover’s disease, ano An important application is the integration of non-trigonometric functions: Latitude is used together with longitude to specify the precise location of features on the surface of the Earth.


Member feedback about GD: Gudermannin formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. The angle depends on the segment length a between the right angle and the vertex of the angle of parallelism.

Gudermannian function

The early drama of the hyperbolic functions”, Functon Magazine 77 1 February A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons. Navigation Revolvy Brain revolvybrain. List of exponential topics topic This is a list of exponential topics, by Wikipedia page. This means that an identity is an equality between functions that are differently defined.

Hopefully then a known integral form would appear or the denominator could be series expanded. The inverse hyperbolic fujction are: The Gudermannian function Gerry Myerson. The Gudermannian functionnamed after Christoph Gudermann —relates the circular functions and hyperbolic functions without explicitly using complex numbers.

Many thanks, I am going to study your answer.