An Introduction To Hypergeometric Supertrigonometric And Superhyperbolic Functions
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An Introduction To Hypergeometric Supertrigonometric And Superhyperbolic Functions
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Author : Xiao-Jun Yang
language : en
Publisher: Academic Press
Release Date : 2021-01-23
An Introduction To Hypergeometric Supertrigonometric And Superhyperbolic Functions written by Xiao-Jun Yang and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-23 with Mathematics categories.
An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering. - Provides a historical overview for a family of the special polynomials - Presents a logical investigation of a family of the hypergeometric series - Proposes a new family of the hypergeometric supertrigonometric functions - Presents a new family of the hypergeometric superhyperbolic functions
Towards Ulam Type Multi Stability Analysis
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Author : Safoura Rezaei Aderyani
language : en
Publisher: Springer Nature
Release Date : 2024-04-29
Towards Ulam Type Multi Stability Analysis written by Safoura Rezaei Aderyani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-29 with Computers categories.
The main target of this book is to present a new concept of Ulam-type stability, i.e., multi-stability, through the classical, well-known special functions and to obtain the best approximation error estimates by a different concept of perturbation stability including fuzzy approaches for uncertainty considerations. This stability allows us to obtain diverse approximations depending on various special functions that are initially chosen and to evaluate maximal stability and minimal error which enable us to obtain a unique optimal solution of functional equations, inequalities, and fractional equations. Stability analysis in the sense of the Ulam and its different kinds has received considerable attention from the researchers. However, how to effectively generalize the Ulam stability problems and to evaluate optimized controllability and stability are new issues. The multi-stability not only covers the previous concepts but also considers the optimization of the problem and provides a comprehensive discussion of optimizing the different types of the Ulam stabilities of mathematical models used in the natural sciences and engineering disciplines with fuzzy attitudes. Besides, this book also deals with nonlinear differential equations with various boundary conditions or initial value problems, based on the matrix Mittag-Leffler function, fixed point theory, as well as Babenko's approach to study uniqueness and existence of solutions. In general, the benefits for the readers can be concluded as follows: 1. Evaluates maximal stability with minimal error to get a unique optimal solution. 2. Discusses an optimal method of the alternative to study existence, uniqueness, and different types of Ulam stabilities under special consideration of the fuzzy approaches. 3. Delves into the new study of boundary value problems of fractional integro-differential equations with integral boundary conditions and variable coefficients.
Theory And Applications Of Special Functions For Scientists And Engineers
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Author : Xiao-Jun Yang
language : en
Publisher: Springer Nature
Release Date : 2022-01-14
Theory And Applications Of Special Functions For Scientists And Engineers written by Xiao-Jun Yang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-14 with Mathematics categories.
This book provides the knowledge of the newly-established supertrigonometric and superhyperbolic functions with the special functions such as Mittag-Leffler, Wiman, Prabhakar, Miller-Ross, Rabotnov, Lorenzo-Hartley, Sonine, Wright and Kohlrausch-Williams-Watts functions, Gauss hypergeometric series and Clausen hypergeometric series. The special functions can be considered to represent a great many of the real-world phenomena in mathematical physics, engineering and other applied sciences. The audience benefits of new and original information and references in the areas of the special functions applied to model the complex problems with the power-law behaviors. The results are important and interesting for scientists and engineers to represent the complex phenomena arising in applied sciences therefore graduate students and researchers in mathematics, physics and engineering might find this book appealing.
Theory Of Hypergeometric Functions
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Author : Kazuhiko Aomoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-21
Theory Of Hypergeometric Functions written by Kazuhiko Aomoto 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 2011-05-21 with Mathematics categories.
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.
The H Function
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Author : A.M. Mathai
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-10
The H Function written by A.M. Mathai 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 2009-10-10 with Science categories.
TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.
Lie Theory And Special Functions
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Author : Miller
language : en
Publisher: Academic Press
Release Date : 1968
Lie Theory And Special Functions written by Miller and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Lie Theory and Special Functions
Fuzzy Fractional Differential Operators And Equations
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Author : Tofigh Allahviranloo
language : en
Publisher: Springer Nature
Release Date : 2020-06-15
Fuzzy Fractional Differential Operators And Equations written by Tofigh Allahviranloo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-15 with Technology & Engineering categories.
This book contains new and useful materials concerning fuzzy fractional differential and integral operators and their relationship. As the title of the book suggests, the fuzzy subject matter is one of the most important tools discussed. Therefore, it begins by providing a brief but important and new description of fuzzy sets and the computational calculus they require. Fuzzy fractals and fractional operators have a broad range of applications in the engineering, medical and economic sciences. Although these operators have been addressed briefly in previous papers, this book represents the first comprehensive collection of all relevant explanations. Most of the real problems in the biological and engineering sciences involve dynamic models, which are defined by fuzzy fractional operators in the form of fuzzy fractional initial value problems. Another important goal of this book is to solve these systems and analyze their solutions both theoretically and numerically. Given the content covered, the book will benefit all researchers and students in the mathematical and computer sciences, but also the engineering sciences.
Stochastic Models Information Theory And Lie Groups Volume 1
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Author : Gregory S. Chirikjian
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-02
Stochastic Models Information Theory And Lie Groups Volume 1 written by Gregory S. Chirikjian 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 2009-09-02 with Mathematics categories.
This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.
Fourier Acoustics
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Author : Earl G. Williams
language : en
Publisher: Academic Press
Release Date : 1999-06-16
Fourier Acoustics written by Earl G. Williams and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-16 with Mathematics categories.
Fourier Acoustics develops the theory of sound radiation completely from the viewpoint of Fourier analysis. This powerful perspective of sound radiation provides the reader with a comprehensive and practical understanding which will enable him or her to diagnose and solve sound and vibration problems of the 21st century. As a result of this perspective, Fourier Acoustics is able to present thoroughly and simply, for the first time in book form, the theory of nearfield acoustical holography, an important technique which has revolutionized the measurement of sound. The book includes: The physics of wave propagation and sound radiation in homogeneous media Acoustics, such as radiation of sound, and radiation from vibrating surfaces Inverse problems, for example the thorough development of the theory of nearfield acoustical holography Mathematics of specialized functions, such as spherical harmonics The author is an internationally recognized acoustician whose pioneering research in the field of nearfield acoustical holography has impacted acoustics research and development throughout the world. Dr. Williams' research has been formally recognized by NRL as one of its most innovative technologies over the past 75 years. Relying little on material outside the book, Fourier Acoustics will be invaluable as a graduate level text as well as a reference for researchers in academia and industry. The book is unique amongst acoustics texts, it is well illustrated and it includes exercises to enforce the theory.
Fast Multipole Methods For The Helmholtz Equation In Three Dimensions
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Author : Nail A Gumerov
language : en
Publisher: Elsevier
Release Date : 2005-01-27
Fast Multipole Methods For The Helmholtz Equation In Three Dimensions written by Nail A Gumerov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-27 with Mathematics categories.
This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a broad audience of researchers. This is exactly what the authors of this book have accomplished. For this reason, it will be a valuable reference for a broad audience of engineers, physicists and applied mathematicians. - The Only book that provides comprehensive coverage of this topic in one location - Presents a review of the basic theory of expansions of the Helmholtz equation solutions - Comprehensive description of both mathematical and practical aspects of the fast multipole method and it's applications to issues described by the Helmholtz equation