Last edited by Taulmaran
Wednesday, May 6, 2020 | History

4 edition of Path functions and generalized basic hypergeometric functions found in the catalog.

# Path functions and generalized basic hypergeometric functions

## by Kevin W. J. Kadell

Written in English

Subjects:
• Functions, Hypergeometric.,
• Partitions (Mathematics),
• Generating functions.

• Edition Notes

Classifications The Physical Object Statement Kevin W.J. Kadell. Series Memoirs of the American Mathematical Society -- no.360 LC Classifications QA3, QA353.H9 Pagination p. cm Open Library OL22601370M ISBN 10 0821824201

Beginning with simple integer-valued functions, the book progresses to polynomials, exponential, trigonometric, Bessel, and hypergeometric functions, and many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while stressing utility by:   In this article, the univalent Meijer's G-functions are classified into three types. Certain integral, differential or differintegral transformations preserving the univalence of the Meijer's G-functions, have been discussed. This classification and transformations are based on Kiryakova's studies in representing the generalized hypergeometric functions as fractional differintegral operators Cited by: 3.

Keywords little q-Jacobi polynomials basic hypergeometric functions bilateral basic hypergeometric functions q-binomial theorem Rogers-Fine symmetric function Ramanujan's 1ψ1 sum Heine's q-Gauss sum and 2ϕ1 transformation q-Chu-Vandermonde sum q-Saalschütz sum nonterminating sum and Macdonald Bidenharn-Louck Heckman-Opdam Koornwinder and Sahi-Knop polynomialsCited by: 2. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms.

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. such generalized hypergeometric functions to generalized hypergeometric integrals, commonly referred to as Barnes-type integrals (because of presence of many other integral representations for hypergeometric functions), and to basic hypergeometric functions when the quotient u(n+ 1)/u(n) of two successive terms is a rationalCited by: 3.

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### Path functions and generalized basic hypergeometric functions by Kevin W. J. Kadell Download PDF EPUB FB2

Get this from a library. Path functions and generalized basic hypergeometric functions book functions and generalized basic hypergeometric functions. [Kevin W J Kadell] -- Path functions and their basic properties are obtained by extending the constructive theory of partition generating functions developed by Sylvester, Durfee, Andrews and others.

Path functions also. Genre/Form: Electronic books: Additional Physical Format: Print version: Kadell, Kevin W.J., Path functions and generalized basic hypergeometric functions /.

Title (HTML): Path Functions and Generalized Basic Hypergeometric Functions Author(s) (Product display): Kevin J Kadell Book Series Name: Memoirs of the American Mathematical Society.

basic hypergeometric series and applications Download basic hypergeometric series and applications or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get basic hypergeometric series and applications book now. This site is like a library, Use search box in the widget to get ebook that you want.

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. 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.

The master functions of the trace functions for sp(2n) are similar new multiple path hypergeometric functions. Analogous multiple path hypergeometric functions for orthogonal Lie algebras are. hypergeometric functions for those who want to have a quick idea of some main facts on hypergeometric functions.

It is the startig of a book I intend to write on 1-variable hyper-geometric functions. As time progressed this informal note attracted increasing Size: KB. Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: Chapters: Meijer G-function, Frobenius solution to the hypergeometric equation, Hypergeometric function, Generalized hypergeometric function, Confluent hypergeometric function, Appell series, Binomial transform, Basic hypergeometric series, Lauricella Author: Source: Wikipedia.

The basic hypergeometric functions satisfy a recurrence relation of the formula with rational functions. The formula can be considered as a partial of Wimp's result for the generalized.

The generalized hypergeometric series is sometimes just called the hypergeometric series, though this term also sometimes just refers to the Gaussian hypergeometric series.

Generalized hypergeometric functions include the (Gaussian) hypergeometric function and the confluent hypergeometric function as special cases, which in turn have many. ible in terms of generalized hypergeometric functions. A complex asymptotic process based on singularity analysis and integral representations akin to Mellin transforms leads to explicit values for various structure constants related to path length, retrieval costs, and storage occupation.

@ John Wiley & Sons, Inc. INTRODUCTION. Hypergeometric functions have been increasingly present in several disciplines including Statistics, but there is much confusion on their proper uses, as well as on their existence and domain of definition.

In this article, we try to clarify several points and give a general overview of the topic, going from the univariate case to the matrix case, in one and then in several by: 3. Download a handbook of generalized special functions for statistical and physical sciences or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get a handbook of generalized special functions for statistical and physical sciences book now. This site is like a library, Use search box in the widget to. In mathematics, the G-function was introduced by Cornelis Simon Meijer () as a very general function intended to include most of the known special functions as particular cases.

This was not the only attempt of its kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's G-function was able to include those as particular cases as well.

In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.

It 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 equation. ital formula book for generalized hypergeometric functions and the OpenXM/fb authoring tools.

In the proposed format, mathematical formulae are stored with references and other information as annotated digital formula in a collection called a for-mula book. The structure of the proposed formula book is. A solid reference on the subject. Material on generalized hypergeometric functions (starting with Gauss' hypergeometric function) is presented followed by the q analogy's.

The material is advanced and is well written with a tight and readable typeface. The introduction to q series will satisfy the beginner. Path functions and generalized basic hypergeometric functions - Kevin W. Kadell: MEMO/ The Selberg trace formula for ${\rm PSL}_2({\bf R})^n$ - Isaac Y. Efrat: MEMO/ Yang-Mills fields and extension theory - Robert Pool.

Using the scaling properties of the process, we represent the Laplace transforms of various hitting times as certain continued fractions that appear in Ramanujan’s “lost” notebook and evaluate these continued fractions in terms of basic hypergeometric functions (that is, q-analogues of classical hypergeometric functions).

The process has. () Branching rules for symmetric functions and sl n basic hypergeometric series. Advances in Applied Mathematics() Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation by: hypergeometric series we derive, using indeﬁnite summation, several summa-tion, transformation, and expansion formulas for multibasic theta hypergeo-metric series.

Some of the identities presented here generalize corresponding formulas given in Chapter 11 of the Gasper and Rahman book [Basic hyperge-File Size: KB.The paper by Salvatore Pincherle (Professor of Mathematics at the University of Bologna) on generalized hypergeometric functions is revisited.

We point out the pioneering contribution of the Italian mathematician towards the Mellin–Barnes integrals based on the duality principle between linear differential equations and linear difference Cited by: