**Author**: Yudell L. Luke

**Publisher:**Academic Press

**ISBN:**0080955606

**Category:**Mathematics

**Page:**348

**View:**702

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# Search Results for: the-special-functions-and-their-approximations-volume-1

**Author**: Yudell L. Luke

**Publisher:** Academic Press

**ISBN:** 0080955606

**Category:** Mathematics

**Page:** 348

**View:** 702

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.

**Author**: Yudell L. Luke

**Publisher:** N.A

**ISBN:** N.A

**Category:** Approximation theory

**Page:** N.A

**View:** 530

**Author**: Yudell L. Luke

**Publisher:** N.A

**ISBN:** N.A

**Category:** Approximation theory

**Page:** N.A

**View:** 7429

**Author**: Yudell L. Luke

**Publisher:** N.A

**ISBN:** N.A

**Category:** Mathematics

**Page:** 349

**View:** 9352

**Author**: Yudell L. Luke

**Publisher:** Academic Press

**ISBN:** 0080955614

**Category:** Computers

**Page:** 484

**View:** 7046

Special Functions and Their Approximations: v. 2

**Author**: F. W. J. Olver

**Publisher:** Academic Press

**ISBN:** 148326744X

**Category:** Mathematics

**Page:** 588

**View:** 1665

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.

**Author**: Yudell L. Luke

**Publisher:** Academic Press

**ISBN:** 1483262456

**Category:** Mathematics

**Page:** 586

**View:** 5932

Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind. Numerical coefficients for Chebyshev expansions of the more common functions are tabulated. Other chapters contain polynomial and rational approximations for certain class of G-functions, the coefficients in the early polynomials of these rational approximations, and the Padé approximations for many of the elementary functions and the incomplete gamma functions. The remaining chapters describe the development of analytic approximations and expansions. This book will prove useful to mathematicians, advance mathematics students, and researchers.

**Author**: Theodore J. Rivlin

**Publisher:** Courier Corporation

**ISBN:** 9780486640693

**Category:** Mathematics

**Page:** 150

**View:** 6025

Mathematics of Computing -- Numerical Analysis.

**Author**: N. N. Lebedev

**Publisher:** Courier Corporation

**ISBN:** 0486139891

**Category:** Mathematics

**Page:** 308

**View:** 7619

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.

**Author**: Johan de De Villiers

**Publisher:** Springer Science & Business Media

**ISBN:** 9491216503

**Category:** Mathematics

**Page:** 406

**View:** 1815

The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter

**Author**: Richard Courant,D. Hilbert

**Publisher:** John Wiley & Sons

**ISBN:** 3527617221

**Category:** Science

**Page:** 575

**View:** 6054

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.

**Author**: Annie A.M. Cuyt,Vigdis Petersen,Brigitte Verdonk,Haakon Waadeland,William B. Jones

**Publisher:** Springer Science & Business Media

**ISBN:** 9781402069499

**Category:** Mathematics

**Page:** 431

**View:** 8072

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!
*A Journey in Dialogues*

**Author**: Frank Blume,Calvin Piston

**Publisher:** Jones & Bartlett Learning

**ISBN:** 9780763728779

**Category:** Computers

**Page:** 869

**View:** 3989

Applied Calculus For Scientists And Engineers Is An Invitation To An Intellectual Journey Into A Discipline That Has Profoundly Influenced The Development Of Western Civilization For More Than Three Hundred Years. The Author Takes A Functional Pedagogical Approach Through The Use Of A Dialogue-Based Writing Style That Is Uniquely Suited To Make Transparent The Essential Problem-Solving Strategies. As The Text Follows Simplicio And Sophie In Their Struggle To Understand The Teacher's Explanations, Students Will Find That Many Of Their Own Difficulties Are Adequately Addressed And Elegantly Resolved. The Text Is Centered On The Idea That Good Teaching Must Bring Knowledge To Life. True To This Premise, The Author Has Taken Great Care To Present All Mathematical Subjects Within The Context Of Stimulating Applications That Cover A Wide Range Of Topics In Science And Engineering. Also Included Are Engaging Discussions Of The Historical And Philosophical Background That Gave The Discipline Of Calculus Its Present Shape. Indeed, It Is The Central Focus On Applications Combined With A Commitment To Very High Standards Of Expository Writing That Sets This Book Apart From The Competition.

**Author**: Isidor Pavlovich Natanson

**Publisher:** N.A

**ISBN:** N.A

**Category:** Approximation theory

**Page:** N.A

**View:** 5707

*Derivatives, Integrals, Series and Other Formulas*

**Author**: Yury A. Brychkov

**Publisher:** CRC Press

**ISBN:** 158488956X

**Category:** Mathematics

**Page:** 704

**View:** 2471

Because of the numerous applications involved in this field, the theory of special functions is under permanent development, especially regarding the requirements for modern computer algebra methods. The Handbook of Special Functions provides in-depth coverage of special functions, which are used to help solve many of the most difficult problems in physics, engineering, and mathematics. The book presents new results along with well-known formulas used in many of the most important mathematical methods in order to solve a wide variety of problems. It also discusses formulas of connection and conversion for elementary and special functions, such as hypergeometric and Meijer G functions.

**Author**: Alvaro Lozano-Robledo

**Publisher:** American Mathematical Soc.

**ISBN:** 0821852426

**Category:** Mathematics

**Page:** 195

**View:** 5900

Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular forms, and $L$-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.

**Author**: Philip J. Davis

**Publisher:** Courier Corporation

**ISBN:** 0486624951

**Category:** Mathematics

**Page:** 393

**View:** 6489

Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.
*In Honor of Gradimir V. Milovanović*

**Author**: Walter Gautschi,Giuseppe Mastroianni,Themistocles Rassias

**Publisher:** Springer Science & Business Media

**ISBN:** 1441965947

**Category:** Mathematics

**Page:** 482

**View:** 8611

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines; - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in the computational and applied sciences.
*with Formulas, Graphs, and Mathematical Tables*

**Author**: Milton Abramowitz,Irene A. Stegun

**Publisher:** Courier Corporation

**ISBN:** 0486158241

**Category:** Mathematics

**Page:** 1046

**View:** 8901

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.

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