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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Introduction The effect of following a rhumb line course on the surface of a globe was first discussed by the Portuguese mathematician Pedro Nunes inin his Treatise in Defense of the Marine Chart, with further mathematical development by Thomas Harriot in the s.

The mnemonic “All Science Teachers are Crazy” lists the basic functions ‘All’, sin, tan, cos which are positive fro Also written as arccosec.

Bell polynomials Bender—Dunne polynomial Jacob Bernoulli: 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.

Karapetoff published the first part of his Engineering Applications of Higher Mat In a footnote, Hobson gives several other names and some historical notes. Wilson B Ernest William Barnes: Visual proof of the Pythagorean identity. Lines of constant latitude, or parallels, run east—west as circles parallel to the equator. Anyway, back to Don Katze’s question.

real analysis – The Gudermannian function and the Apéry’s constant – Mathematics Stack Exchange

Note that the last one is freely available on-line. His researches into spherical geometry and special functions focused on particular cases, so that he did not receive the cred Hopefully then a known integral form would appear or the denominator could be series expanded. Angle Revolvy Brain revolvybrain.


At this point, let’s dispense with ‘theta’ and ‘u’ and just use ‘x’ and ‘y’. Outline of trigonometry topic Trigonometry is a branch of mathematics that studies the relationships between the sides and the angles in triangles.

Gudermannian function topic Graph of the Gudermannian function The Gudermannian function, named after Christoph Gudermann —relates the circular functions and hyperbolic functions without explicitly using complex numbers.

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Gudermannian — from Wolfram MathWorld

The Gudermannian functionnamed after Christoph Gudermann —relates the circular functions and hyperbolic functions without explicitly using complex numbers.

Member feedback about Vladimir Karapetoff: 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. Latitude topic A graticule on the Earth as a sphere or an ellipsoid. The graticule gudermanjian the latitude and longitude of points on the surface.

Back to Topic List. Elementary special functions Revolvy Brain revolvybrain.

The basic hyperbolic functions are: Briefly, geodetic latitude at a point is the angle formed by the vector perpendicular or normal to the ellipsoidal sur He called it the “transcendent angle,” and it went by various names until when Arthur Cayley suggested it be given its current name as a tribute to Gudermann’s work in the s on the theory of special functions.

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Without trying all that hard, here are some things I googled up that are on-line: This post, whose main body is a post I made on 11 September in another group, is intended in the same spirit as the post I made yesterday, which is at http: Member feedback about List of exponential topics: So, for example, landmasses such as Greenland and Antarctica appear much larger th A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons.