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Generalized Bessel Functions of the First Kind by Árpád Baricz Pdf
This volume studies the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. It presents interesting geometric properties and functional inequalities for these generalized functions.
Introduction to Bessel Functions by Frank Bowman Pdf
Self-contained text, useful for classroom or independent study, covers Bessel functions of zero order, modified Bessel functions, definite integrals, asymptotic expansions, and Bessel functions of any real order. 226 problems.
Series of Bessel and Kummer-Type Functions by Árpád Baricz,Dragana Jankov Maširević,Tibor K. Pogány Pdf
This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.
Bessel Functions and Their Applications by B G Korenev Pdf
Bessel functions are associated with a wide range of problems in important areas of mathematical physics. Bessel function theory is applied to problems of acoustics, radio physics, hydrodynamics, and atomic and nuclear physics. Bessel Functions and Their Applications consists of two parts. In Part One, the author presents a clear and rigorous intro
Advances in Algebra and Analysis by V. Madhu,A. Manimaran,D. Easwaramoorthy,D. Kalpanapriya,M. Mubashir Unnissa Pdf
This volume is the first of two containing selected papers from the International Conference on Advances in Mathematical Sciences, Vellore, India, December 2017 - Volume I. This meeting brought together researchers from around the world to share their work, with the aim of promoting collaboration as a means of solving various problems in modern science and engineering. The authors of each chapter present a research problem, techniques suitable for solving it, and a discussion of the results obtained. These volumes will be of interest to both theoretical- and application-oriented individuals in academia and industry. Papers in Volume I are dedicated to active and open areas of research in algebra, analysis, operations research, and statistics, and those of Volume II consider differential equations, fluid mechanics, and graph theory.
Generalized Associated Legendre Functions And Their Applications by Iryna Fedotova,Nina Virchenko Pdf
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 Harmonic Analysis and Wavelet Packets by Khalifa Trimeche Pdf
The book presents a more comprehensive treatment of transmutation operators associated with the Bessel operator, and explores many of their properties. They are fundamental in the complete study of the Bessel harmonic analysis and the Bessel wavelet packets. Many applications of these theories and their generalizations have been injected throughout the text by way of a rich collection of problems and references. The results and methods in this book should be of interest to graduate and researchers working in special functions such as Fourier analysis, hypergroup and operator theories, differential equations, probability theory and mathematical physics. Background materials are given in adequate detail to enable a graduate student to proceed rapidly from the very basics of the frontier of research in the area of generalized harmonic analysis and wavelets.
Special Functions & Their Applications by N. N. Lebedev Pdf
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.
Theory of Fundamental Bessel Functions of High Rank by Zhi Qi Pdf
In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
Special Functions of Mathematics for Engineers by Larry C. Andrews Pdf
Modern engineering and physical science applications demand a thorough knowledge of applied mathematics, particularly special functions. These typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics. This text systematically introduces special functions and explores their properties and applications in engineering and science.
Partial Differential Equations by Rustum Choksi Pdf
While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate students from different cohorts with one sole purpose: to facilitate a proficiency in many core concepts in PDEs while enhancing the intuition and appreciation of the subject. For mathematics students this will in turn provide a solid foundation for graduate study. A recurring theme is the role of concentration as captured by Dirac's delta function. This both guides the student into the structure of the solution to the diffusion equation and PDEs involving the Laplacian and invites them to develop a cognizance for the theory of distributions. Both distributions and the Fourier transform are given full treatment. The book is rich with physical motivations and interpretations, and it takes special care to clearly explain all the technical mathematical arguments, often with pre-motivations and post-reflections. Through these arguments the reader will develop a deeper proficiency and understanding of advanced calculus. While the text is comprehensive, the material is divided into short sections, allowing particular issues/topics to be addressed in a concise fashion. Sections which are more fundamental to the text are highlighted, allowing the instructor several alternative learning paths. The author's unique pedagogical style also makes the text ideal for self-learning.
The Fifth International Conference on General Inequalities was held from May 4 to May 10, 1986, at the Mathematisches Forschungsinstitut Oberwolfach (Black Forest, Germany). The organizing committee consisted of W.N. Everitt (Birmingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec served efficiently an'd enthusiastically as secretary to the con ference. The meeting was attended by 50 participants from 16 countries. In his opening address, W. Walter had to report on the death of five colleagues who had been active in the area of inequali ties and who had served the mathematical community: P.R. Beesack, G. Polya, D.K. Ross, R. Bellman, G. Szegö. He made special mention of G. Polya, who had been the last surviving author of the book InequaZities (Cambridge University Press, 1934), who died at the age of 97 years and whose many and manifold contributions to mathematics will be recorded elsewhere, in due course. Inequalities continue to play an important and significant role in nearly all areas of mathematics. The interests of the participants to this conference reflected the many different fields in which both classical and modern inequalities continue to influence developments in mathematics. In addition to the established fields, the lectures clearly indicated the importance of inequalities in functional analysis, eigenvalue theory, con vexi ty., number theory, approximation theory, probability theory, mathematical prograrnrning and economics.
