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From Bessel To Multi Index Mittag Leffler Functions

Author : Jordanka Paneva-Konovska
ISBN : 1786340887
Genre : Bessel functions
File Size : 54.17 MB
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"The main concern in the book is the convergence of series in such functions in the complex plane, and the author provides a unified approach to handle this matter." Fractional Calculus and Applied Analysis Bessel and Mittag-Leffler functions are prominent within mathematical and scientific fields due to increasing interest in non-conventional models within applied mathematics. Since the analytical solutions of many differential and integral equations of arbitrary order can be written as series of special functions of fractional calculus, they are now unavoidable tools for handling various mathematical models of integer or fractional order. From Bessel to Multi-Index Mittag-Leffler Functions analyzes this through the study of enumerable families of different classes of special functions. Enumerable families are considered and the convergence of series is investigated. Providing a unified approach to the classical power series, analogues of the classical results for the power series are obtained, and the conclusion is that each of the considered series has a similar convergence behavior to a power series. Also studied are various properties of the Bessel and Mittag-Leffler functions and their generalizations, including estimations, asymptotic formulae, fractional differentiation and integration operators.
Category: Bessel functions

Elementary Introduction To The Theory Of Pseudodifferential Operators

Author : Xavier Saint Raymond
ISBN : 9781351452922
Genre : Mathematics
File Size : 66.85 MB
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In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is strictly mathematical in the sense that it contains precise definitions, statements of theorems and complete proofs, and follows the usual method of pure mathematics. The book explains the origin of the theory (i.e., Fourier transformation), presents an elementary construcion of distribution theory, and features a careful exposition of standard pseudodifferential theory. Exercises, historical notes, and bibliographical references are included to round out this essential book for mathematics students; engineers, physicists, and mathematicians who use partial differential equations; and advanced mathematics instructors.
Category: Mathematics

Table Of Integrals Series And Products

Author : I. S. Gradshteyn
ISBN : 9781483265643
Genre : Mathematics
File Size : 61.68 MB
Format : PDF, Kindle
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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.
Category: Mathematics

C Coding Standards

Author : Herb Sutter
ISBN : 0132654423
Genre : Computers
File Size : 33.22 MB
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Consistent, high-quality coding standards improve software quality, reduce time-to-market, promote teamwork, eliminate time wasted on inconsequential matters, and simplify maintenance. Now, two of the world's most respected C++ experts distill the rich collective experience of the global C++ community into a set of coding standards that every developer and development team can understand and use as a basis for their own coding standards. The authors cover virtually every facet of C++ programming: design and coding style, functions, operators, class design, inheritance, construction/destruction, copying, assignment, namespaces, modules, templates, genericity, exceptions, STL containers and algorithms, and more. Each standard is described concisely, with practical examples. From type definition to error handling, this book presents C++ best practices, including some that have only recently been identified and standardized-techniques you may not know even if you've used C++ for years. Along the way, you'll find answers to questions like What's worth standardizing--and what isn't? What are the best ways to code for scalability? What are the elements of a rational error handling policy? How (and why) do you avoid unnecessary initialization, cyclic, and definitional dependencies? When (and how) should you use static and dynamic polymorphism together? How do you practice "safe" overriding? When should you provide a no-fail swap? Why and how should you prevent exceptions from propagating across module boundaries? Why shouldn't you write namespace declarations or directives in a header file? Why should you use STL vector and string instead of arrays? How do you choose the right STL search or sort algorithm? What rules should you follow to ensure type-safe code? Whether you're working alone or with others, C++ Coding Standards will help you write cleaner code--and write it faster, with fewer hassles and less frustration.
Category: Computers

A Treatise On The Theory Of Bessel Functions

Author : G. N. Watson
ISBN : 0521483913
Genre : Mathematics
File Size : 66.67 MB
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This monumental 1995 treatise by the late Professor G. N. Watson wil be indispensable to mathematicians and physicists.
Category: Mathematics

Handbook Of Mathematical Functions

Author : Milton Abramowitz
ISBN : 9780486158242
Genre : Mathematics
File Size : 35.36 MB
Format : PDF, Docs
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A classic resource for working with special functions, standard trig, and exponential logarithmic definitions and extensions, it features 29 sets of tables, some to as high as 20 places.
Category: Mathematics