Numerical Methods For Special Functions
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Numerical Methods For Special Functions
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Author : Amparo Gil
language : en
Publisher: SIAM
Release Date : 2007-01-01
Numerical Methods For Special Functions written by Amparo Gil and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. This book provides an up-to-date overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. Not only are standard and simple parameter domains considered, but methods valid for large and complex parameters are described as well. The first part of the book (basic methods) covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations. Its focus is on the computation of special functions; however, it is suitable for general numerical courses. Pseudoalgorithms are given to help students write their own algorithms. In addition to these basic tools, the authors discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions, Padé approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).
Asymptotics And Special Functions
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Author : F. W. J. Olver
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Asymptotics And Special Functions written by F. W. J. Olver 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.
Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.
The Special Functions And Their Approximations
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Author : Yudell L. Luke
language : en
Publisher: Academic Press
Release Date : 1969
The Special Functions And Their Approximations written by Yudell L. Luke and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
A detailed and self-contained and unified treatment of many mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. many common features of the Bessel functions, Legendre functions, incomplete gamma functions, confluent hypergeometric functions, as well as of otherw, can be derived. Hitherto, many of the material upon which the volumes are based has been available only in papers scattered throughout the literature.
Computation Of Special Functions
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Author : Shanjie Zhang
language : en
Publisher: Wiley-Interscience
Release Date : 1996-07-26
Computation Of Special Functions written by Shanjie Zhang and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-26 with Mathematics categories.
Computation of Special Functions is a valuable book/software package containing more than 100 original computer programs for the computation of most special functions currently in use. These include many functions commonly omitted from available software packages, such as the Bessel and modified Bessel functions, the Mathieu and modified Mathieu functions, parabolic cylinder functions, and various prolate and oblate spheroidal wave functions. Also, unlike most software packages, this book/disk set gives readers the latitude to modify programs according to the special demands of the sophisticated problems they are working on. The authors provide detailed descriptions of the program's algorithms as well as specific information about each program's internal structure.
Introduction To Asymptotics And Special Functions
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Author : F. W. J. Olver
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Introduction To Asymptotics And Special Functions written by F. W. J. Olver 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.
Introduction to Asymptotics and Special Functions is a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable are discussed, along with contour integrals and differential equations with regular and irregular singularities. The Liouville-Green approximation is also considered. Comprised of seven chapters, this volume begins with an overview of the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on integrals of a real variable. Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions. A chapter devoted to the Liouville-Green approximation tackles asymptotic properties with respect to parameters and to the independent variable, eigenvalue problems, and theorems on singular integral equations. This monograph is intended for students needing only an introductory course to asymptotics and special functions.
Special Functions
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Author : George E. Andrews
language : en
Publisher: Cambridge University Press
Release Date : 1999
Special Functions written by George E. Andrews and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
Numerical Analysis Or Numerical Method In Symmetry
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Author : Clemente Cesarano
language : en
Publisher: MDPI
Release Date : 2020-02-21
Numerical Analysis Or Numerical Method In Symmetry written by Clemente Cesarano and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-21 with Mathematics categories.
This Special Issue focuses mainly on techniques and the relative formalism typical of numerical methods and therefore of numerical analysis, more generally. These fields of study of mathematics represent an important field of investigation both in the field of applied mathematics and even more exquisitely in the pure research of the theory of approximation and the study of polynomial relations as well as in the analysis of the solutions of the differential equations both ordinary and partial derivatives. Therefore, a substantial part of research on the topic of numerical analysis cannot exclude the fundamental role played by approximation theory and some of the tools used to develop this research. In this Special Issue, we want to draw attention to the mathematical methods used in numerical analysis, such as special functions, orthogonal polynomials, and their theoretical tools, such as Lie algebra, to study the concepts and properties of some special and advanced methods, which are useful in the description of solutions of linear and nonlinear differential equations. A further field of investigation is dedicated to the theory and related properties of fractional calculus with its adequate application to numerical methods.
Calculation Of Special Functions
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Author : C. G. van der Laan
language : en
Publisher:
Release Date : 1984
Calculation Of Special Functions written by C. G. van der Laan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Error functions categories.
Practical Numerical Methods With C
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Author : Jack Xu
language : en
Publisher: UniCAD
Release Date : 2019
Practical Numerical Methods With C written by Jack Xu and has been published by UniCAD this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.
The second edition of this book builds all the code example within a single project by incorporating new advancements in C# .NET technology and open-source math libraries. It also uses C# Interactive Window to test numerical computations without compiling or running the complete project code. The second edition includes three new chapters, including "Plotting", Fourier Analysis" and "Math Expression Parser". As in the first edition, this book presents an in-depth exposition of the various numerical methods used in real-world scientific and engineering computations. It emphasizes the practical aspects of C# numerical methods and mathematical functions programming, and discusses various techniques in details to enable you to implement these numerical methods in your .NET application. Ideal for scientists, engineers, and students who would like to become more adept at numerical methods, the second edition of this book covers the following content: - Overview of C# programming. - The mathematical background and fundamentals of numerical methods. - plotting the computation results using a 3D chart control. - Math libraries for complex numbers and functions, real and complex vector and matrix operations, and special functions. - Numerical methods for generating random numbers and random distribution functions. - Various numerical methods for solving linear and nonlinear equations. - Numerical differentiation and integration. - Interpolations and curve fitting. - Optimization of single-variable and multi-variable functions with a variety of techniques, including advanced simulated annealing and evolutionary algorithms. - Numerical techniques for solving ordinary differential equations. - Numerical methods for solving boundary value problems. - Eigenvalue problems. - Fourier analysis. - mathematical expression parser and evaluator. In addition, this book provides testing examples for every math function and numerical method to show you how to use these functions and methods in your own .NET applications in a manageable and step-by-step fashion. Please visit the author's website for more information about this book at https://drxudotnet.com https://drxudotnet.com and https://gincker.com.
Advances In Special Functions Of Fractional Calculus Special Functions In Fractional Calculus And Their Applications In Engineering
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Author : Praveen Agarwal
language : en
Publisher: Bentham Science Publishers
Release Date : 2023-04-11
Advances In Special Functions Of Fractional Calculus Special Functions In Fractional Calculus And Their Applications In Engineering written by Praveen Agarwal and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-11 with Mathematics categories.
In recent years, special functions have been developed and applied in a variety of fields, such as combinatorics, astronomy, applied mathematics, physics, and engineering due to their remarkable properties. This volume expands our understanding of special functions by highlighting recent trends in numerical analysis. Interesting applications of special functions and partial differential equations are demonstrated by 15 chapters. Many chapters highlight the importance of numerical techniques and the results of complex analysis. Contributions in the book emphasize the mathematical treatment of questions arising in natural sciences and engineering, particularly those that involve novel problems and their solutions. This volume is a timely update for mathematicians and researchers interested in advanced numerical methods and computational techniques used to solve complex problems List of Chapters 1. Modified Adaptive Synchronization and Anti Synchronization method for Fractional order chaotic systems with uncertain parameters 2. Improved generalized differential transform method for a class of linear non homogeneous ordinary fractional differential equation 3. Incomplete K2-Function 4. Some Results On Incomplete Hypergeometric Functions 5. Transcendental Bernstein Series: Interpolation and Approximation 6. Some Sufficient Conditions For Uniform Convexity Of Normalized 1F2 Function 7. From Abel continuity theorem to Paley-Wiener theorem… 8. A New Class of Truncated Exponential-Gould-Hopper basedGenocchi Polynomials 9. Computational preconditioned Gauss-Seidel via half-sweep approximation to Caputo's time fractional differential equations 10. Krasnoselskii-type Theorems for Monotone Operators in Ordered Banach Algebra with Applications in Fractional Differential Equations and Inclusion 11. General fractional order quadratic functional integral equations: Existence, properties of solutions and some of its Applications 12.Nonlinear set-valued delay functional integral equations of Volterra-Stieltjes type: Existence of solutions, continuous dependence and applications 13.Certain Saigo Fractional Derivatives Of Extended Hypergeometric Functions 14. Some Erdelyi-kober Fractional Integrals Of The Extended Hypergeometric Functions 15. On solutions of Kinetic Model by Sumudu transform