2 edition of **Generalized hypergeometric functions** found in the catalog.

Generalized hypergeometric functions

Singh, Shobh Nath.

- 174 Want to read
- 14 Currently reading

Published
**1993**
by Radha Publications in New Delhi
.

Written in English

- Hypergeometric functions.

**Edition Notes**

Includes bibliographical references (p. [165]-176).

Statement | Shobh Nath Singh. |

Classifications | |
---|---|

LC Classifications | QA353.H9 S56 1993 |

The Physical Object | |

Pagination | v, 176 p. ; |

Number of Pages | 176 |

ID Numbers | |

Open Library | OL1062040M |

ISBN 10 | 8185484651 |

LC Control Number | 93907541 |

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. 53 ON HYPERGEOMETRIC SERIES ASSOCIATED WITH THE GENERALIZED ZETA FUNCTIONS Maged G. Bin-Saad1,* and Amani M. Hanballa1 1 Department of Mathematics, Aden University, Aden, Kohrmaksar, ,Yemen E-mail:[email protected] *Corresponding author Abstract In this work we will introduce and study a generalized zeta function of the general Hurwitz –.

by r [2] while studying generating functions of hypergeometric functions in the year From the seventies onwards, Weisners group-theoretic method has been utilized by researchers while deriving gener-ating functions of various special functions. Khanna I.K. and Bhagavan V.S. [7] obtained the generating relations for generalized. Generating functions for the generalized Appell function 7 [7] D. M. Lee, A. K. Rathie, R. K. Parmar and Y. S. Kim, Generalization of extended Beta function, hypergeometric and con.

The generalized hypergeometric functions with p numerator and q denominator parameters is defined by. p F q Higher Transcendental Functions, Volume 1, McGraw-Hill Book Company, New York, (). [3] Exton, H., Multiple Hypergeometric Integrals, Halsted Press, New York, ().Author: Shantha Kumari, J. Prathima, Arjun K. Rathie. Publisher Summary. This chapter presents the generalized hypergeometric function p F q and the G-function is significant as numerous special functions appearing in applied mathematics are special cases or are closely , a result involving a G-function becomes a master or a key formula from which a very large number of results can be deduced for Bessel functions.

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Generalized Hypergeometric Functions. Transformations and group theoretical aspects. This detailed monograph outlines the fundamental relationships between the hypergeometric function and special functions. In nine comprehensive chapters, Dr. Rao and Dr. Lakshminarayanan present a unified approach to the study of special functions of.

Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis. ebook Generalized hypergeometric functions book is temporary and does not include ownership of the ebook.

Only valid for books with an ebook version. Book Description 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 by: A central theme is the development of the Laplace transform in Generalized hypergeometric functions book context and its application to spaces of functions associated with hypergeometric functions.

Consequently, this book represents a significant further development of the theory and demonstrates how the Boyarksy principle may be given a cohomological by: 2 Background on hypergeometric functions In this section, we will introduce properties of the generalized hypergeometric function that will be exploited in this project.

The motivation for computing hypergeometric functions will be discussed, with details given of some of the practical applications of these functions. Hypergeometric functions have occupied a significant position in mathematics for over two centuries.

This monograph, by one of the foremost experts, is concerned with the Boyarksy principle which expresses the analytic properties of a certain proto-gamma function. Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences.

Authors; A. Mathai; R. Saxena; Book. Citations; k Downloads; Part of the Lecture Notes in Mathematics book series (LNM, volume ) Log in to check access. Buy eBook. USD Computable representations of a G-function in the. Hundreds of thousands of mathematical results derived at Wolfram Research give the Wolfram Language unprecedented strength in the transformation and simplification of hypergeometric functions.

This allows hypergeometric functions for the first time to take their place as a practical nexus between many special functions\[LongDash]and makes possible a major new level of algorithmic calculus. CoNTEMPORARY MATHEMATICS Hypergeometric Functions on Domains of Positivity, Jack Polynomials, The paper used in this book is acid-free and falls within the guidelines Generalized hypergeometric functions and Laguerre polynomials in two variables ZHIMIN YAN The density of λ will go in terms of a H-function.

The H-function is more or less the most generalized special function in real scalar variable case and it is defined by the following Mellin. 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. 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. Internal Report SUF–PFY/96–01 Stockholm, 11 December 1st revision, 31 October last modiﬁcation 10 September Hand-book on STATISTICAL. Summary: Hypergeometric functions have occupied a significant position in mathematics for over two centuries.

This monograph is concerned with the Boyarsky principle which expresses the analytic properties of a certain proto-gamma function. The generalized Gauss function is also used in mathematical statistics and the basic analogues of the Gauss functions have applications in the field of number theory.

Dr Slater's treatment leads on from a discussion of the Gauss functions to the basic hypergeometric functions, the hypergeometric integrals, bilateral series and Appel : Lucy Joan Slater. pergeometric functions, the Appell and Lauricella functions and Horn’s functions.

They are called A-hypergeometric functions and they provide a beautiful and elegant basis of a theory of hypergeometric functions in several variables. For an introduction to the subject we refer the reader to [33], [5] or the book by Saito, Sturmfels and File Size: KB.

John Wallis (–), in his book Arithmatica Infinitorium (), extended the ordinary geometric series to the hypergeometric series: with the nth term given by: which later became, with b = 1, the Slater Lucy J Generalized Hypergeometric Functions. When q + 1 hypergeometric series diverges for all z ≠ 0 unless it is a polynomial (i.e.

the function has nonpositive integers in the first list of parameters). In this case, the hypergeometric function can be defined as the analytic continuation of the (customarily undefined) hypergeometric series through a contour integral (see DLMF ()). Hypergeometric Functions: HypergeometricPFQ[{a 1,a 2,a 3},{b 1,b 2},z] ( formulas) Primary definition (2 formulas) Specific values ( formulas) General characteristics (23 formulas) Series representations (40 formulas) Integral representations (5 formulas).

OCLC Number: Notes: Includes indexes. Description: xiii, pages: illustrations ; 24 cm: Contents: The Gauss function --The generalized Gauss function --Basic hypergeometric functions --Hypergeometric integrals --Basic hypergeometric integrals --Bilateral series --Basic bilateral series --Appell series --Basic Appell sibility: by Lucy Joan Slater.

Hypergeometric functions A hypergeometric function is the sum of a hypergeometric series, which is deﬁned as follows. the radius of convergence ρ of the hypergeometric series is given by q is called a generalized hypergeo-metric function.

Then the words ”hypergeometric function File Size: 90KB.Generalized Hypergeometric Functions. Definition and Analytic Properties; Derivatives and Contiguous Functions; Argument Unity; Integral Representations and Integrals; Transformations of Variable; Relations to Other Functions; Differential Equations; Zeros; Expansions in Series of F q p Functions.Full Description: " Reading Generalized Hypergeometric Series can create great peace and inner peace.

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