In mathematics, the Gaussian or ordinary hypergeometric function 2 F 1 (a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting is a solution of a second-order linear ordinary differential equation (ODE). Every second-order linear ODE with three regular singular points can be transformed into this. Book Description: The subject of this book is the higher transcendental function known as the confluent hypergeometric function. In the last two decades this function has taken on an ever increasing significance because of its use in the application of mathematics to . More applications—including those of generalized spheroidal wave functions and confluent Heun functions in mathematical physics, astrophysics, and the two-center problem in molecular quantum mechanics—can be found in Leaver and Slavyanov and Lay (, Chapter 4). . Mathematical function, suitable for both symbolic and numerical manipulation. The function has the integral representation. HypergeometricU [a, b, z] has a branch cut discontinuity in the complex plane running from to. For certain special arguments, HypergeometricU .

hypergeometric functions of Gauss, Horn, Appell, and Lauricella. We will emphasize the alge-braic methods of Saito, Sturmfels, and Takayama to construct hypergeometric series and the connection with deformation techniques in commutative algebra. We end with a brief discussion of the classiﬁcation problem for rational hypergeometric functions. Special Functions – wi The book which will be used in this course is: George E. Andrews, Richard Askey & Ranjan Roy: Special Functions. Encyclopedia of Mathematics and its Applicati Cambridge University Press. Hardback, , ISBN Bessel functions and confluent hypergeometric functions: Chapter 5: Orthogonal. M. R. Dotsenko, On some applications of Wrights hypergeometric function, Dokladi Na Bolgarskata Akademiya Na Naukite 44(6) (), 13 – M. Dotsenko, On some applications of Wright’s hypergeometric function, Comptes Rendus de l’Academie Bulgare des Sciences 44 (), 13 – Instead of this hodge-podge of results, one could get for less than half the price the beautiful and insightful book by Hochstadt (The Functions of Mathematical Physics) which covers Orthogonal Polynomials and the Hypergeometric and Confluent Hypergeometric Functions and also Bessel Functions and more.

Confluent hypergeometric function of the second kind: U(,,)= E+ This answer is the same as KummerU(,,) in Maple Find many great new & used options and get the best deals for Encyclopedia of Mathematics and Its Applications Ser.: Special Functions by Richard Askey, George E. Andrews and Ranjan Roy (, Perfect) at the best online prices at eBay! Free shipping for many products! (The factor of in the Denominator is present for historical reasons of notation.) The function corresponding to, is the first hypergeometric function to be studied (and, in general, arises the most frequently in physical problems), and so is frequently known as ``the'' hypergeometric equation. To confuse matters even more, the term ``hypergeometric function'' is less commonly . For some special choice of black hole parameters, the Green function reduces to simpler hypergeometric or confluent hypergeometric functions. Two of the authors of the paper quoted above had calculated Green's functions in terms of the Heun function in an earlier paper, Exact Green's Functions from Conformal Gravity [].