Download or read book Handbook of Hypergeometric Integrals written by Harold Exton and published by . This book was released on 1978-01-01 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Hypergeometric Integrals written by Harold Exton and published by . This book was released on 1978 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Hypergeometric Functions written by Kazuhiko Aomoto and published by Springer Science & Business Media. This book was released on 2011-05-21 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy a holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy a holonomic system of linear difference equations with respect to the exponents. These are deduced from Grothendieck-Deligne’s rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoff’s classical theory on analytic difference equations on the other.
Download or read book The Confluent Hypergeometric Function written by Herbert Buchholz and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. There is no doubt that this trend will continue until the general theory of confluent hypergeometric functions becomes familiar to the majority of physicists in much the same way as the cylinder functions, which were previously less well known, are now used in many engineering and physical problems. This book is intended to further this development. The important practical significance of the functions which are treated hardly demands an involved discussion since they include, as special cases, a number of simpler special functions which have long been the everyday tool of the physicist. It is sufficient to mention that these include, among others, the logarithmic integral, the integral sine and cosine, the error integral, the Fresnel integral, the cylinder functions and the cylinder function in parabolic cylindrical coordinates. For anyone who puts forth the effort to study the confluent hypergeometric function in more detail there is the inestimable advantage of being able to understand the properties of other functions derivable from it. This gen eral point of view is particularly useful in connection with series ex pansions valid for values of the argument near zero or infinity and in connection with the various integral representations.
Download or read book Handbook of Integrals and Series written by Yury A. Brychkov and published by Chapman and Hall/CRC. This book was released on 2017-10-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The second volume of the set contains formulas devoted to mathematical physics, including the Meijer G-function and properties of hypergeometric functions. Using these tools, readers can evaluate and simplify numerous new integrals and sums.
Download or read book Handbook of Special Functions written by Yury A. Brychkov and published by CRC Press. This book was released on 2008-05-28 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of the numerous applications involved in this field, the theory of special functions is under permanent development, especially regarding the requirements for modern computer algebra methods. 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 problems. It also discusses formulas of connection and conversion for elementary and special functions, such as hypergeometric and Meijer G functions.
Download or read book Arrangements and Hypergeometric Integrals written by Peter Orlik and published by . This book was released on 2007 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Basic Hypergeometric Series written by George Gasper and published by . This book was released on 2011-02-25 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant revision of classic reference in special functions.
Download or read book The Hypergeometric Approach to Integral Transforms and Convolutions written by S.B. Yakubovich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to develop a new approach which we called the hyper geometric one to the theory of various integral transforms, convolutions, and their applications to solutions of integro-differential equations, operational calculus, and evaluation of integrals. We hope that this simple approach, which will be explained below, allows students, post graduates in mathematics, physicists and technicians, and serious mathematicians and researchers to find in this book new interesting results in the theory of integral transforms, special functions, and convolutions. The idea of this approach can be found in various papers of many authors, but systematic discussion and development is realized in this book for the first time. Let us explain briefly the basic points of this approach. As it is known, in the theory of special functions and its applications, the hypergeometric functions play the main role. Besides known elementary functions, this class includes the Gauss's, Bessel's, Kummer's, functions et c. In general case, the hypergeometric functions are defined as a linear combinations of the Mellin-Barnes integrals. These ques tions are extensively discussed in Chapter 1. Moreover, the Mellin-Barnes type integrals can be understood as an inversion Mellin transform from the quotient of products of Euler's gamma-functions. Thus we are led to the general construc tions like the Meijer's G-function and the Fox's H-function.
Download or read book Handbook of Mathematical Functions written by Milton Abramowitz and published by Courier Corporation. This book was released on 1965-01-01 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive summary of mathematical functions that occur in physical and engineering problems
Download or read book Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory written by Chester Snow and published by . This book was released on 1952 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory written by Chester Snow and published by . This book was released on 1942 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Integral Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2008-02-12 with total page 1143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa
Download or read book Handbook of Integral Transforms of Higher Transcendental Functions written by Oleg Igorevich Marichev and published by Ellis Horwood. This book was released on 1983 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Table of Integrals Series and Products written by Daniel Zwillinger and published by Elsevier. This book was released on 2007-02-23 with total page 1220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom. - Fully searchable CD that puts information at your fingertips included with text- Most up to date listing of integrals, series andproducts - Provides accuracy and efficiency in work
Download or read book Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences written by A. M. Mathai and published by Springer. This book was released on 2006-11-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Handbook of Generalized Special Functions for Statistical and Physical Sciences written by A. M. Mathai and published by Oxford University Press, USA. This book was released on 1993 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complicated generalized special functions such as Meijer's G-functions and functions of matrix arguments are here presented at a level suitable for every potential user. This handbook is thus a valuable reference source and a manual for researchers and advanced students in mathematical statistics, mathematical physics, several branches of mathematics, engineering problems, econometrics, and various applied areas where transcendental functions are used.
