The Mathematica GuideBook for Symbolics (text and code fully tailored with Mathematica 5.1) is the fourth volume of the Mathematica GuideBooks, a comprehensive and detailed print and electronic reference for Mathematica. It introduces the reader to symbolic computations using Mathematica and enables readers to understand, perform, and optimize sophisticated symbolic computations. It includes detailed discussions of the most frequent symbolic operations such as equation solving, differentiation, series expansion, and integration with more than 200 fully worked examples from physics, mathematics and computer graphics. Functions from algebra and analysis, as well as orthogonal polynomials and special functions of mathematical physics are also discussed. An indispensable resource for practitioners, professionals, and researchers in mathematics, computer science, engineering and other scientific disciplines, The Mathematica GuideBook for Symbolics will find a natural place on the bookshelf as an essential reference work. The Guidebooks in general give the user a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The four GuideBooks contain about 25,000 Mathematica inputs, representing more that 75,000 lines of commented Mathematica code. They also have more than 4,500 graphics, 150 animations, 11,000 references and 1,000 exercises.

Introduction and Orientation

I. Symbolic computations: *Remarks *Manipulation of polynomials *Manipulations of rational functions of polynomials *Manipulations of trigonometric expressions *Systems of linear and nonlinear equations *Classical analysis *Differential equations *Integral transforms and generalized functions *Three applications *Overview

II Classical orthogonal polynomials: *Remarks *General properties of orthogonal polynomials *Hermite polynomials *Jacobi polynomials *Gegenbauer polynomials *Laguerre polynomials *Legendre polynomials *Chebyshev polynomials T *Chebyshev polynomials U *Relationships among the orthogonal polynomials *Overview

III Classical special functions: *Remarks/Introduction *Gamma, beta, and polygamma functions *Error functions and Fresnel integrals *Sine, cosine, exponential, and logarithmic integral functions *Bessel and airy functions *Legendre functions *Hypergeometric functions *Elliptic integrals *Elliptic functions *ProductLog function *Mathieu functions * Additional special functions *Solution of quintics with hypergeometric functions *Overview

Index