The confluent hypergeometric function with special emphasis on its applications.

by Herbert Buchholz

Publisher: Springer in Berlin, Heidelberg, New York

Written in English
Published: Pages: 238 Downloads: 298
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Subjects:

  • Hypergeometric functions.

Edition Notes

Statement(Translation from the German.) Translated by H. Lichtblau and K. Wetzel.
SeriesSpringer tracts in natural philosophy, v. 15
Classifications
LC ClassificationsQA351 .B813
The Physical Object
Paginationxviii, 238 p.
Number of Pages238
ID Numbers
Open LibraryOL5684582M
LC Control Number69016291

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 [].

The confluent hypergeometric function with special emphasis on its applications. by Herbert Buchholz Download PDF EPUB FB2

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 physical and technical problems.

The Confluent Hypergeometric Function: with Special Emphasis on its Applications (Springer Tracts in Natural Philosophy (15)) Softcover reprint of the original 1st ed. Edition by Herbert Buchholz (Author), H. Lichtblau (Translator), K. Wetzel (Translator) & 0 moreCited by: 63 [1, 7].—Herbert Buchholz, The Confluent Hypergeometric Function, with Special Emphasis on its Applications, translated by H.

Lichtblau & K. Wetzel, Springer-Verlag, New York,xviii + pp., 24 cm. Price $ This translation of the original edition published in German is a valuable book. Notebook which overlaps the present book in significant ways.

Research on g-hypergeometric series is significantly more active now than when Fine began his researches. There are now major interactions with Lie algebras, combinatorics, special functions, and number theory. I am immensely pleased that Fine has finally decided to publish this mono­.

Introduction 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 physical and technical problems.

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 physical and technical problems.

The Confluent Hypergeometric Function. With Special Emphasis on its Applications. Bln., Springer 9 figs. XVIII, p. OCloth.

(slightly rubbed).- Springer Tracts in Natural Philosophy, Ownership inscription on flyleaf, otherwise in very good condition. BUCHHOLZ, Herbert. Table in Lakshminarayanan and Varadarajan gives a list of various special functions in terms of the hypergeometric functions, including many not described here (LV, chap pages –89).

Also, their figure gives a block diagram that summarizes succinctly the intimate relationship between the special functions and their. The Confluent Hypergeometric Function: with Special Emphasis on its Applications, by Herbert Buchholz.

The first chapter is entitled The Various Forms of the Differential Equation for the Confluent Hypergeometric Function and the Definitions of their Solutions.

In just the past thirty years several new special functions and applications have been discovered. This treatise presents an overview of the area of special functions, focusing primarily on the.

In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular term confluent refers to the merging of singular points of families of differential equations; confluere is Latin for "to flow together".

In accordance with the discussion given there, we obtain the second integral of equation () by replacing the function F in () by some other linear combination of two terms whose sum is, according to (d), the confluent hypergeometric function. These functions, as a part of the theory of confluent hypergeometric functions, are important special functions and their closely related ones are widely used in physics and engineering.

Moreover, generalized Beta functions [2, 3] have played a pivotal role in the advancement of further research and have proved to be exemplary in nature. The emphasis is upon explicit solutions to Volterra convolution integral equations of the first kind in which the kernels are explicit special functions.

Sections cover kernels from algebraic through Bessel and on to generalized hypergeometric functions. Table 1 is arranged in roughly the same order. Gauss hypergeometric function and extended confluent hypergeometric function and for p = q, λ = σ = τ = 1, they reduce to () and () respectively.

Integral Representations of F λ ; σ,τ. Chapter 13 Confluent Hypergeometric Functions. Applications. Mathematical Applications; Physical Applications; Computation. Methods of Computation; Tables; Release date A printed companion is available.

Software Special Notation. In this paper, we aim to present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the.

Applications on Generalized Hypergeometric and Confluent Hypergeometric Functions. International Journal of Mathematical Analysis and Applications.

Vol. 5, No. 1,pp. Abstract Recently, some generalizations of the generalized famous special functions (e.g. Gamma. Other topics include q-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems.

The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. The confluent and Gauss hypergeometric functions are examples of special func- tions, whose theory and computation are prominent in the scientific literature [3, 6, 40, 53, 57, 58, 62, 73, 95, 97, ].

Andrews, Askey, Roy "Special Functions" Cambridge () has three chapters totalling pages devoted explicitly to hyper geometric functions and confluent hypergeometric functions, and they arise frequently in other parts. It is a really interesting book. The Confluent Hypergeometric Function with Special Emphasis on its Applications.

New York: Springer-Verlag, Morse, P. and Feshbach, H. Methods of Theoretical Physics, Part I. q-SPECIAL FUNCTIONS 3 for this series (and for its sum when it converges) assuming c6= 0 ; 1; 2. This is the (ordinary) hypergeometric series or the Gauss hypergeometric series.

The series converges absolutely for jzj0, see Exercise1. Many important functions, such as. Special functions, natural generalizations of the elementary functions, have been studied for centuries.

The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise. Hypergeometric Functions by John Pearson J Some examples of hypergeometric functions from practical applications K List of code written for this project Bibliography 1 Introduction The computation of the hypergeometric function pF q, a special function encountered in a variety of applications, is frequently sought.

However. Confluent hypergeometric functions are the solutions of the confluent hypergeometric equation. Such equation can be obtained from the hypergeometric equation by the confluence of two of its sigularities.

Confluent hypergeometric functions include as special cases the commonly used Bessel functions, Hermite functions, Laguerre functions, etc. Calculates confluent hypergeometric function of the first kind or Kummer's function M(a,b,z).

In just the past thirty years several An introduction to the theory of Bessel functions Watson: An introduction to the theory of orthogonal polynomials qSeries: Bessel functions and confluent hypergeometric functions Chapter 5: Special orthogonal polynomials Chapter 7: The exam grade is the final grade Supplementary material in de form of pdf-documents: Functins products.

With the help of this new generalized Pochhammer symbol, we then introduce an extension of the generalized hypergeometric function "rF"s with r numerator and s denominator parameters. Finally, we present a systematic study of the various fundamental properties of the class of the generalized hypergeometric functions introduced here.

Askey and R. Roy “Special Functions”, Encyclopedia of Mathematics and its Applicati Cambridge University Press, The book by N.M. Temme “Special functions: an introduction to the classical functions of mathematical physics”, John Wiley & Sons, Inc.

Indefinite Hypergeometric Summations The W-Z Method Contiguous Relations and Summation Methods 4 Bessel Functions and Confluent Hypergeometric Functions The Confluent Hypergeometric Equation Barnes's Integral for ${}_1F_1$ Whittaker Functions Examples of ${}_1F_1$ and Whittaker Functions Bessel's Equation and.Mathematical function, suitable for both symbolic and numerical manipulation.

The function has the series expansion. For certain special arguments, Hypergeometric1F1 automatically evaluates to exact values. Hypergeometric1F1 can be evaluated to arbitrary numerical precision.

Hypergeometric1F1 automatically threads over lists.Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions.