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of the hypergeometric function by means of the differential equation it satisfies. Riemann showed that the second-order differential equation for 2F1(z)...

confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where...

mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular...

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives...

the following we solve the second-order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand...

an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation, is a linear homogeneous ordinary differential equation with variable coefficients...

dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations. Deterministic...

{dw}{dz}}-ab\,w=0.} It is known as the hypergeometric differential equation. When c is not a positive integer, the substitution w = z...

rational functions of the variables (e.g. the hypergeometric equation). Algebraic differential equations are widely used in computer algebra and number...

In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are...

differential equations that have received specific names, area by area. Ablowitz-Kaup-Newell-Segur (AKNS) system Clairaut's equation Hypergeometric differential...

mathematical physics the Knizhnik–Zamolodchikov equations, or KZ equations, are linear differential equations satisfied by the correlation functions (on the...

occurs, for example, between the hypergeometric equation, with three regular singular points, and the Bessel equation which is in a sense a limiting case...

}{4j^{2}(1-1728j)^{2}}}f=0.\,} This equation can be cast into the form of the hypergeometric differential equation. It has two linearly independent solutions...

Romanovski polynomials solve the following version of the hypergeometric differential equation Curiously, they have been omitted from the standard textbooks...

starting from known special-case solutions of the Gauss hypergeometric differential equation). Also, approximation (11) has been found only recently....

turbine equation Euler transform used to accelerate the convergence of an alternating series and is also frequently applied to the hypergeometric series...

singular points, such as the Lamé equation or the hypergeometric differential equation, can be transformed into this equation by a change of variable. Coalescence...

arbitrary ordinary differential equations of even order. Weyl applied his theory to Carl Friedrich Gauss's hypergeometric differential equation, thus obtaining...

The Schrödinger equation of this potential can be solved analytically, by transforming it into a hypergeometric differential equation. The radial part...