# Handbook of hypergeometric integrals

theory, applications, tables, computer programs by Harold Exton

Publisher: Ellis Horwood, Publisher: Halsted Press, a division of J. Wiley in Chichester [Eng.], New York

Written in English

## Subjects:

• Hypergeometric functions.

## Edition Notes

Classifications The Physical Object Statement Harold Exton. Series Ellis Horwood series in mathematics and its applications LC Classifications QA353.H9 E93 1978 Pagination 316 p. ; Number of Pages 316 Open Library OL4739319M ISBN 10 0470263423 LC Control Number 78040120

By expanding $(1 - tz) ^ {- \alpha }$ into a binomial series and using contour integrals for the beta-function, other integral representations can be obtained. The integral (3) and other similar formulas defining an analytic function of $z$ which is single-valued throughout the $z$- plane can also be used as analytic continuations of. ‎Despite the increasing use of computers, the basic need for mathematical tables continues. Tables serve a vital role in preliminary surveys of problems before programming for machine operation, and they are indispensable to thousands of engineers and scientists without access to machines. Because of. Marichev is the author or coauthor of 70 papers and eight books, including his Handbook of Integral Transforms of Higher Transcendental Functions. He wrote the five-volume series Integrals and Series with A. P. Prudnikov and Yu. A. Brychkov. 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.

In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic generalized hypergeometric series is sometimes just called the. Handbook of mathematical formulas and integrals. San Diego: Academic Press, © (OCoLC) Online version: Jeffrey, Alan. Handbook of mathematical formulas and integrals. San Diego: Academic Press, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Alan Jeffrey.   SUMMARY Various representations for incomplete Lipschitz-Hankel integrals of Bessel functions have been given in terms of Kampe de Fiet double hypergeometric functions. Reduction formulas for the double series employed have been given in some cases. ALLEN R. MILLER REFERENCES 1. H. EXTON. "Handbook of Hypergeometnc Integrals," Halsted. Index λ-system Algebra Almost sure convergence Bayes Bernoulli Bernstein inequality Beta distribution function integral random variable Binomial distribution negative binomial random variable Borel-Cantelli Cauchy distribution Central limit theorem history - Selection from Handbook of Probability [Book].

This book is a compendium of mathematical formulas, tables, and graphs. It contains a table of analytical integrals, differential equations, and numerical series; and includes tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration, and techniques for point interpolation and.   Books. Publishing Support. Login. Reset your password. If you have a user account, you will need to reset your password the next time you login. You . Schaum's outlines mathematical handbook of formulas and tables Series Schaum's outline series Note Includes index. ISBN (pbk: acid-free paper) (pbk: acid-free paper) (basic e-book). F (a, b; c; z) is the hypergeometric function. a, b, and c are parameters, z is a variable in the complex plane. As the function is defined by a series, it is sometimes called the hypergeometric series. A similar function, the confluent hypergeometric function, is denoted with F (a; b; z). The function can also be represented by integrals.

## Handbook of hypergeometric integrals by Harold Exton Download PDF EPUB FB2

Handbook of hypergeometric integrals: Theory, applications, tables, computer programs (Ellis Horwood series in mathematics and its applications) by Harold Exton (Author) › Visit Amazon's Harold Exton Page. Find all the books, read about the author, and more. See search. Handbook of Hypergeometric Integrals: Theory, Applications, Tables, Computer Programs Harold Exton Ellis Horwood, - Hypergeometric functions - pages.

Handbook of hypergeometric integrals—theory, application, tables, computer programs, by Harold Exton, Ellis Horwood Limited, Chichester, Author: J. Murphy. Download Handbook Of Hypergeometric Integrals full book in PDF, EPUB, and Mobi Format, get it for read on your Kindle device, PC, phones or tablets.

Handbook Of Hypergeometric Integrals full free pdf books. On an Integral Involving Bessel Polynomials and -Function of Two Variables and Its Application. Turkish Journal of Analysis and Number Theory. ; 2(4) doi: /tjant Correspondence to: Yashwant Singh, Department of Mathematics,Government College, Kaladera, Jaipur, Rajasthan.

Cite this article as: Buckland, W. J Oper Res Soc () First Online 01 May ; DOI Author: W. Buckland. Handbook Of Integrals and Series Set (Volumes I and II): Handbook of Integrals and Series: Special Functions, Volume II (Volume 2) 1st Edition including the Meijer G-function and properties of hypergeometric functions.

Using these tools, readers can evaluate and simplify numerous new integrals. Handbook of Hypergeometric - Free ebook download as PDF File .pdf), Text File .txt) or view presentation slides online. Originally a page pocket-sized book, known as the Rubber Handbook, the CRC Handbook of Chemistry and Physics comprises 2, pages of critically evaluated data.

An essential resource for scientists around the world, the Handbook is now available in print, eBook, and online formats. Internal Report SUF–PFY/96–01 Stockholm, 11 December 1st revision, 31 October last modiﬁcation 10 September Hand-book on STATISTICAL.

International Standard Book Number (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been. Acknowledgements: This chapter is based in part on Chapter 15 of Abramowitz and Stegun by Fritz Oberhettinger.

The author thanks Richard Askey and Simon Ruijsenaars for many helpful recommendations. Handbook of Hypergeometric Integrals: Theory, Applications, Tables, Computer Programs (Mathematics & Its Applications) (Mathematics and Its Applications).

Serious students of mathematical physics will find it useful to invest in a good handbook of integrals and tables. My favorite is the classic Handbook of Mathematical Functions, With Formu- las, Graphs, and Mathematical Tables(AMS55), edited by Mil- ton Abramowitz and Irene A.

Stegun. The book presents new results along with well-known formulas used in many of the most important mathematical methods in order to solve a wide variety of problems.

Read "Handbook of hypergeometric integrals—theory, application, tables, computer programs, by Harold Exton, Ellis Horwood Limited, Chichester, No. of pages:price £15, International Journal for Numerical Methods in Engineering" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.

Get this from a library. Handbook of hypergeometric integrals: theory, applications, tables, computer programs. [Harold Exton]. Description This handbook presents many known results as well as new classes of integrals, series, power expansions, and productions of elementary and special functions.

It shows how modern computer algebra methods are used to solve various problems in science and engineering. Handbook of Special Functions book.

Derivatives, Integrals, Series and Other Formulas Handbook of Special Functions book. Derivatives, Integrals, Series and Other Formulas. By Yury A. Brychkov. Edition 1st Edition. First Published eBook Published 28 May Representations of Hypergeometric Functions and of the Meijer G Function.

Purchase Table of Integrals, Series, and Products - 8th Edition. Print Book & E-Book. ISBNThe correlation function for the Gegenbauer, Chebyshev and Legendre polynomials can be written as a 4F3 hypergeometric function.

For the Jacobi polynomials the result is an F2 Appell function. The numerous applications of special functions in solving many of the more difficult problems in physics, engineering, and mathematics make their development a continuous and evolving process.

Bringing new insight to these functions, the Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas presents new results and includes some known functions for completeness in.

It is shown there that the most effective and the simplest algorithm of analytical integration was made by O.I. Marichev [8, 9, 12]. Later it was realized in the reference-books [, 20]. This algorithm allows us to calculate definite and indefinite integrals of the products of elementary and special functions of hypergeometric type.

This handbook results from a year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full color, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun.

This handbook results from a year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators.

Printed in full color, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Chapter 1. Euler, Fourier, Bernoulli, Maclaurin, Stirling The Integral Test and Euler’s Constant Suppose we have a series X1 k=1 u k of decreasing terms and a decreasing function f such that f(k)=u k, k=1;2;3;Also assume fis positive, continuous for x 1, and lim x!1.

John Wallis (–), in his book Arithmatica Infinitorium (), extended the ordinary A more recent tabulation is the NIST handbook of Mathematical Functions by Olver, Lozier, Boisvert and Clark. The reader is The beta integral method and hypergeometric transformations.

Hypergeometric Functions 4. Legendre Functions 5. Bessel Functions 6. Spherical Harmonics Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research.

The book also discusses extensively the functions of two variables in partial differentiation and multiple integrals. The book. Handbook of Mathematical Formulas and Integrals. Book • Third Edition • The updated Handbook is an essential reference for researchers and students in applied mathematics, engineering, and physics.

It provides quick access to important formulas, relations, and methods from algebra, trigonometric and exponential functions. Exton, H., Handbook of Hypergeometric Integrals. Theory, Applications, Tables, Computer Programs. Chichester, Ellis Horwood Ltd.

Distributors: John Wiley & Sons. Complex hypergeometric function 2F1 for complex a,b,c,andz, by direct integration of the hypergeometric equation in the complex plane. The branch cut is taken to lie along the real axis, Re z>1.

INTEGER kmax,nbad,nok EXTERNAL bsstep,hypdrv COMPLEX z0,dz,aa,bb,cc,y(2) COMMON /hypg/ aa,bb,cc,z0,dz COMMON /path/ kmax Used by odeint. kmax=0. The Handbook of Special Functions provides in-depth coverage of special functions, which are used to help solve many of the most difficult problems in physics, engineering, and mathematics.

The book presents new results along with well-known formulas used in many of the most important mathematical methods in order to solve a wide variety of.The purpose of this handbook is to supply a collection of mathematical formulas and tables which will prove to be valuable to students and research workers in the fields of mathematics, physics, engineering and other sciences.