Zeta And Q Zeta Functions And Associated Series And Integrals
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Zeta And Q Zeta Functions And Associated Series And Integrals
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Author : Hari M Srivastava
language : en
Publisher: Elsevier
Release Date : 2011-10-11
Zeta And Q Zeta Functions And Associated Series And Integrals written by Hari M Srivastava and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-11 with Mathematics categories.
Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. - Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions
Series Associated With The Zeta And Related Functions
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Author : Hari M. Srivastava
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Series Associated With The Zeta And Related Functions written by Hari M. Srivastava 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 2001 with Mathematics categories.
In recent years there has been an increasing interest in problems involving closed form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) various families of series associated with the Riemann Zeta function ((s), the Hurwitz Zeta function ((s,a), and their such extensions and generalizations as (for example) Lerch's transcendent (or the Hurwitz-Lerch Zeta function) iI>(z, s, a). Some of these developments have apparently stemmed from an over two-century-old theorem of Christian Goldbach (1690-1764), which was stated in a letter dated 1729 from Goldbach to Daniel Bernoulli (1700-1782), from recent rediscoveries of a fairly rapidly convergent series representation for ((3), which is actually contained in a 1772 paper by Leonhard Euler (1707-1783), and from another known series representation for ((3), which was used by Roger Apery (1916-1994) in 1978 in his celebrated proof of the irrationality of ((3). This book is motivated essentially by the fact that the theories and applications of the various methods and techniques used in dealing with many different families of series associated with the Riemann Zeta function and its aforementioned relatives are to be found so far only"in widely scattered journal articles. Thus our systematic (and unified) presentation of these results on the evaluation and representation of the Zeta and related functions is expected to fill a conspicuous gap in the existing books dealing exclusively with these Zeta functions.
Integral Transforms And Operational Calculus
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Author : H. M. Srivastava
language : en
Publisher: MDPI
Release Date : 2019-11-20
Integral Transforms And Operational Calculus written by H. M. Srivastava and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-20 with Technology & Engineering categories.
Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications
Analytic Number Theory Approximation Theory And Special Functions
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Author : Gradimir V. Milovanović
language : en
Publisher: Springer
Release Date : 2014-07-08
Analytic Number Theory Approximation Theory And Special Functions written by Gradimir V. Milovanović and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.
Generalized Mathieu Series
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Author : Živorad Tomovski
language : en
Publisher: Springer Nature
Release Date : 2021-11-15
Generalized Mathieu Series written by Živorad Tomovski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-15 with Mathematics categories.
The Mathieu series is a functional series introduced by Émile Léonard Mathieu for the purposes of his research on the elasticity of solid bodies. Bounds for this series are needed for solving biharmonic equations in a rectangular domain. In addition to Tomovski and his coauthors, Pogany, Cerone, H. M. Srivastava, J. Choi, etc. are some of the known authors who published results concerning the Mathieu series, its generalizations and their alternating variants. Applications of these results are given in classical, harmonic and numerical analysis, analytical number theory, special functions, mathematical physics, probability, quantum field theory, quantum physics, etc. Integral representations, analytical inequalities, asymptotic expansions and behaviors of some classes of Mathieu series are presented in this book. A systematic study of probability density functions and probability distributions associated with the Mathieu series, its generalizations and Planck’s distribution is also presented. The book is addressed at graduate and PhD students and researchers in mathematics and physics who are interested in special functions, inequalities and probability distributions.
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.
Mathematical Analysis In Interdisciplinary Research
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Author : Ioannis N. Parasidis
language : en
Publisher: Springer Nature
Release Date : 2022-03-10
Mathematical Analysis In Interdisciplinary Research written by Ioannis N. Parasidis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-10 with Mathematics categories.
This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.
Ramanujan Summation Of Divergent Series
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Author : Bernard Candelpergher
language : en
Publisher: Springer
Release Date : 2017-09-12
Ramanujan Summation Of Divergent Series written by Bernard Candelpergher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-12 with Mathematics categories.
The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.
Special Functions In Fractional Calculus And Engineering
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Author : Harendra Singh
language : en
Publisher: CRC Press
Release Date : 2023-06-29
Special Functions In Fractional Calculus And Engineering written by Harendra Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-29 with Mathematics categories.
Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations. This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.
Almost Impossible Integrals Sums And Series
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Author : Cornel Ioan Vălean
language : en
Publisher: Springer
Release Date : 2019-05-10
Almost Impossible Integrals Sums And Series written by Cornel Ioan Vălean and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-10 with Mathematics categories.
This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.