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Date : 2001-01-29

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Special Functions Encyclopedia of Mathematics and its ~ Book Description Special functions which include the trigonometric functions have been used for centuries Their role in the solution of differential equations was exploited by Newton and Leibniz and the subject of special functions has been in continuous development ever since

Special functions Encyclopedia of Mathematics ~ In the broad sense a set of several classes of functions that arise in the solution of both theoretical and applied problems in various branches of mathematics In the narrow sense the special functions of mathematical physics which arise when solving partial differential equations by the method of

Special Functions encyclopedia Of Mathematics And Its ~ The book begins with a thorough treatment of the gamma and beta functions that are essential to understanding hypergeometric functions Later chapters discuss Bessel functions orthogonal polynomials and transformations the Selberg integral and its applications spherical harmonics qseries partitions and Bailey chains

ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS ~ Preface page xiii 1 The Gamma and Beta Functions 1 11 The Gamma and Beta Integrals and Functions 2 12 The Euler Reflection Formula 9 13 The Hurwitz and Riemann Zeta Functions 15 14 Stirlings Asymptotic Formula 18 15 Gausss Multiplication Formula for Tmx 22 16 Integral Representations for Log Tx and xjr x 26 17 Kummers Fourier

Encyclopedia of Mathematics and its Applications ~ 159 results in Encyclopedia of Mathematics and its Applications Proof complexity is a rich subject drawing on methods from logic combinatorics algebra and computer science This selfcontained book presents the basic concepts classical results current state of the art and possible future directions in the field

SPECIAL FUNCTIONS WITH APPLICATIONS IN NUMERICAL ANALYSIS ~ The special functions have been studied in several volumes by the collective of mathematicians formed by G E Andrews R Askey and R Roy Cambridge University Press Encyclopedia of Mathematics and its Applications

SPECIAL FUNCTIONS AND THEIR SYMMETRIES Mathematics at Leeds ~ application in integration of systems of nonlinear differential equations and in some areas of numeric analysis and discrete mathematics For this part of the course the main reference is the recent book by Andrews R Askey and R Roy “Special Functions” Encyclopedia of Mathematics and its Applications 71 Cambridge University Press 1999 The book by Temme “Special functions an

Special Functions by George E Andrews Cambridge Core ~ Special functions natural generalizations of the elementary functions have been studied for centuries The greatest mathematicians among them Euler Gauss Legendre Eisenstein Riemann and Ramanujan have laid the foundations for this beautiful and useful area of mathematics

Special functions Wikipedia ~ Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis functional analysis physics or other applications

Special Functions and their Applications ~ functions and Tricomi confluent hypergeometric functions These results are important in the study of the infinite divisibility of the Student and FisherSnedecore distributions