Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory
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Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory
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Author : Chester Snow
language : en
Publisher:
Release Date : 1952
Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory written by Chester Snow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Mathematics categories.
The Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory
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Author : Chester Snow
language : en
Publisher:
Release Date : 1942
The Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory written by Chester Snow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1942 with Hypergeometric functions categories.
The Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory
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Author : Chester Snow
language : en
Publisher:
Release Date : 1952
The Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory written by Chester Snow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Hypergeometric functions categories.
The Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory
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Author : Chester Snow
language : en
Publisher:
Release Date : 1875
The Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory written by Chester Snow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1875 with Functions categories.
Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory
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Author : Chester Snow
language : en
Publisher:
Release Date : 1961
Hypergeometric And Legendre Functions With Applications To Integral Equations Of Potential Theory written by Chester Snow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.
Generalized Associated Legendre Functions And Their Applications
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Author : Iryna Fedotova
language : en
Publisher: World Scientific
Release Date : 2001-04-30
Generalized Associated Legendre Functions And Their Applications written by Iryna Fedotova and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-30 with Mathematics categories.
The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions ρFq, Meijer's G-function, Fox's H-function, etc.Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions.This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, Pm,nκ(z) and Qm,nκ(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. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions.The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions Pm,nκ(z) and Qm,nκ(z), the classes of dual and triple integral equations associated with the function Pm,n-1/2+iς(chα) etc.
Generalized Associated Legendre Functions And Their Applications
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Author : Nina Opanasivna Virchenko
language : en
Publisher: World Scientific
Release Date : 2001
Generalized Associated Legendre Functions And Their Applications written by Nina Opanasivna Virchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions ? Fq, Meijer's G -function, Fox's H -function, etc. Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions. This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, P m, n ? ( z ) and Q m, n ? ( 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. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions. The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions P m, n ? ( z ) and Q m, n ? ( z ), the classes of dual and triple integral equations associated with the function P m, n -1/2+i? (cha) etc. Contents: A General Information on Legendre Functions; The Generalized Associated Legendre Functions; The Series Representations of the Generalized Associated Legendre Functions; Relations Between Different Solutions of the Generalized Legendre Equation. Wronskians of Linearly Independent Solutions; Relations Between Contiguous Generalized Associated Legendre Functions; Differential Operators Generated by the Generalized Associated Legendre Equation; Asymptotic Formulas for the Generalized Associated Legendre Functions in a Neighborhood of Singular Points; Asymptotic Representations of the Generalized Associated Legendre Functions as the Functions of Parameters; Integral Representations of the Generalized Associated Legendre Functions of the First Kind; Integral Representations of the Generalized Associated Legendre Functions of the Second Kind; Zeros of the Generalized Associated Legendre Functions; Connection of the Generalized Associated Legendre Functions with the Jacobi Functions; and other topics. Readership: Graduate students and researchers in mathematics, physics and engineer
Special Functions Their Applications
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Author : N. N. Lebedev
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
Special Functions Their Applications written by N. N. Lebedev and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Mathematics categories.
Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.
Table Of Integrals Series And Products
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Author : I. S. Gradshteyn
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Table Of Integrals Series And Products written by I. S. Gradshteyn and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.
Hypergeometric Functions And Their Applications
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Author : James B. Seaborn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Hypergeometric Functions And Their Applications written by James B. Seaborn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Science categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A wide range of problems exists in classical and quantum physics, engi neering, and applied mathematics in which special functions arise. The procedure followed in most texts on these topics (e. g. , quantum mechanics, electrodynamics, modern physics, classical mechanics, etc. ) is to formu late the problem as a differential equation that is related to one of several special differential equations (Hermite's, Bessel's, Laguerre's, Legendre's, etc. ).