http://link.umsl.edu/portal/Advanced-methods-for-solving-differential/1K5Vb_kFRmY/ WebThis chapter contains sections titled: Definitions and Simple Relations Analytic Continuation The Hypergeometric Differential Equation The Singular Points of the Differential …

Hypergeometric series - Book chapter - IOPscience

In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular singular points to occur anywhere on the Riemann sphere, rather than merely at 0, 1, and $${\displaystyle \infty }$$. … See more The differential equation is given by The regular singular points are a, b, and c. The exponents of the solutions at these regular singular points are, respectively, α; α′, β; β′, and γ; γ′. … See more The P-function possesses a simple symmetry under the action of fractional linear transformations known as Möbius transformations (that are the conformal remappings of the Riemann sphere), or equivalently, under the action of the group GL(2, … See more The solutions are denoted by the Riemann P-symbol (also known as the Papperitz symbol) The standard hypergeometric function may be expressed as See more If the Moebius transformation above moves the singular points but does not change the exponents, the following transformation does not move the singular points but changes the exponents: See more • Method of Frobenius • Monodromy See more WebFeb 9, 2000 · Papperitz equation [14]), whilst it is confluen t hypergeometric when the roots. are coincident. The question naturally appearing is what sort of quantum mechanical prob- phishing attack can occur on

Papperitz equation - Encyclopedia of Mathematics

WebThe Singular Points of the Differential Equation, 114 5.5. The Riemann-Papperitz Equation, 116 5.6. Barnes' Contour Integral for F(a, b; c; z), 119 5.7. Recurrence Relations, 121 5.8. Quadratic Transformations, 122 5.9. Generalized Hypergeometric Functions, 124 5.9.1. A First Introduction to ^-functions, 125 WebPapperitz equation. Recently, Ishkhanyan has pointed out that the Carroll-Hioe model can be understood in terms of the hypergeometric functions by considering a complex-valued path z(t) = (y(t)+i)/2i where y(t) is a real variable [14]. By this complex-valued WebAug 10, 2005 · Download PDF Abstract: This paper provides the solution of the Riemann-Papperitz equation with singular points at z=-i,i.This solution is obtained by mapping the singular points into points 0,infinity. The solution is then obtained in terms of the Gauss hypergeometric function. tsp total distribution