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Monday, August 3, 2020 | History

3 edition of Generalized hypergeometric series. found in the catalog.

# Generalized hypergeometric series.

## by W. N. Bailey

Written in English

Edition Notes

Originally published in 1935 by Cambridge U.P.

The Physical Object ID Numbers Series Cambridge tracts in mathematicsand mathematical physics -- No. 32 Pagination 108p. Number of Pages 108 Open Library OL14880526M ISBN 10 0028407601

Additional Physical Format: Online version: Bailey, Wilfrid Norman, Generalized hypergeometric series. New York, Stechert-Hafner Service Agency, This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, P m,n κ (z) and Q m,n κ (z), which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively.

xiii, pages: 24 cm Includes bibliographical references (pages ) Includes indexes The Gauss function -- The generalized Gauss function -- Basic hypergeometric functions -- Hypergeometric integrals -- Basic hypergeometric integrals -- Bilateral series -- Basic bilateral series -- Appell series -- Basic Appell series. Series representations (31 formulas) Integral representations (5 formulas) Limit representations (2 formulas) Continued fraction representations (2 formulas) Differential equations (17 formulas) Transformations (3 formulas) Identities (31 formulas) Differentiation (37 formulas) Integration (4 formulas) Integral transforms (1 formula).

3- Basic hypergeometric series In mathematics, Heine's basic hypergeometric series, or hypergeometric q-series, are q-analog generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series. A series x n is called hypergeometric if the ratio of successive terms x n+1 /x n is a rational function. Additional Physical Format: Online version: Bailey, Wilfrid Norman, Generalized hypergeometric series. New York, Hafner Pub. Co., (OCoLC)

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### Generalized hypergeometric series by W. N. Bailey Download PDF EPUB FB2

Generalized hypergeometric series (Cambridge tracts in mathematics and mathematical physics No. 32) Paperback – January 1, by Wilfrid Norman Bailey (Author) › Visit Amazon's Wilfrid Norman Bailey Page.

Find all the books, read about the author, and more. See search Author: Wilfrid Norman Bailey. The theory of generalized hypergeometric functions is fundamental in the field of mathematical physics, since all the commonly used functions of analysis (Besse] Functions, Legendre Functions, etc.) are special cases of the general functions.

bilateral series and Appel series. This book was planned jointly with the late Professor W. N Cited by: The number of additions in both and is n, but the number of multiplications reduces from (n − 1)n/2, or O(n 2) for large n → ∞, resulting in a reduction in the computational time required for the numerical evaluation of the generalized hypergeometric series (see chapter 6).

Generalized Hypergeometric Functions. Transformations and group theoretical aspects. Gauss first outlined his studies of the hypergeometric series which has been of great significance in the mathematical modelling of physical phenomena.

This detailed monograph outlines the fundamental relationships between the hypergeometric function and. Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications Book 96) - Kindle edition by Gasper, George, Rahman, Mizan.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications Book 96).Reviews: 2. 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. If $\alpha$ or $\beta$ are zero or negative integers, the series (2) terminates after a finite number of terms, and the hypergeometric function is a polynomial in $z$. If $\gamma = - n$, $n = 0, 1 \dots$ the hypergeometric function is not defined, but.

A difference equation analogue of the generalized hypergeometric differential equation is defined, its contiguous relations are developed, and its relation to numerous well-known classical special.

The term “ hypergeometric series ” was first used by J. Wallis in to refer to a generalization of the geometric series [Dut].Many leading mathematicians of the 18th and 19th centuries, such as Euler, Gauss, Jacobi, Kummer, Fuchs, Riemann, Schwarz and Klein (cf.

[K11, K12]) contributed to the study of hypergeometric Schwarz [Sch] solved the problem of finding those. Generalized Hypergeometric Series. Hardcover – Import, January 1, by Wilfred Norman Bailey (Author) See all formats and editions Hide other formats and editions.

Price New from Used from Hardcover, Import, January 1, "Please retry" — — — Hardcover — Author: Wilfred Norman Bailey. gin by deﬁning Gauss’ 2F1 hypergeometric series, the rF s (generalized) hyper-geometric series, and pointing out some of their most important special cases.

Next we deﬁne Heine’s 2φ1 basic hypergeometric series which contains an addi-tional parameter q, called the base, and then give the deﬁnition and notations for rφ s basic. Abstract. This paper deals with the study of a generalized function of Mittag-Leffler type. Various properties including usual differentiation and integration, Euler(Beta) transforms, Laplace transforms, Whittaker transforms, generalized hypergeometric series form with their several special cases are obtained and relationship with Wright hypergeometric function and Laguerre polynomials is also.

W.N. Bailey: Generalized Hypergeometric Series. Published , Cambridge University Press. Contents Preface Chapter I The hypergeometric series Introduction Pochhammer Hypergeometric 2F1 Chapter II Generalized hypergeometric series.

Further results concerning ordinary hypergeometric series Chapter III Series of type ${}_3F_2$ with unit. H.M. Srivastava, Junesang Choi, in Zeta and q-Zeta Functions and Associated Series and Integrals, The hypergeometric functions can be generalized along the lines of basic (or q-) number, resulting in the formation of q-extensions (or q-analogues).This chapter provides an overview of the q-Extensions of some special functions and polynomials.

These extensions are potentially useful in. Generalized Hypergeometric Functions explores the way in which hypergeometric functions are interlinked with special functions, and it uses group theory to illustrate these relationships.

The application of group theory to the study of special functions is a relatively new approach to the subject area. It is a departure from most of the standard text books, which deal with the special.

The book of Saito, Sturmfels, and Takayama [37] serves as the backbone for these The following two-variable hypergeometric series are particular cases of the so called Horn series [16, page ]. This is a list of 34 bivariate hypergeometric series for which the ratios R.

is the generalized hypergeometric function. Details. Mathematical function, suitable for both symbolic and numerical manipulation. has series expansion, where is the Pochhammer symbol. Hypergeometric0F1, Hypergeometric1F1, Introductory Book.

Wolfram Function Repository. The series converges conditionally if |z| = 1 with z 6= 1 and −1 series diverges if Re(P b i − P a j) ≤ −1. Sometimes the most general hypergeometric function pF q is called a generalized hypergeo-metric function.

Then the words ”hypergeometric function” refer to the special case 2F 1(a,b; c; z. The first five chapters cover basic hypergeometric series and integrals, whilst the next five are devoted to applications in various areas including Askey-Wilson integrals and orthogonal polynomials, partitions in number theory, multiple series, orthogonal polynomials in several variables, and generating functions.

Generalized hypergeometric series by Wilfrid Norman Bailey,The University Press edition, in EnglishPages:. Series representations (40 formulas) Generalized power series (38 formulas) Residue representations (2 formulas).In mathematics, basic hypergeometric series, or q-hypergeometric series, are q-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series.A series x n is called hypergeometric if the ratio of successive terms x n+1 /x n is a rational function of the ratio of successive terms is a rational function of q n, then the series is.Euler’s hypergeometric series are now often called Gauss hypergeometric functions.

The next major contribution came from Rie-mann. In the article [19] from he gave a complete description of the monodromy group for example of a generalized hypergeometric function.