The Mathematica GuideBook for Symbolics

Cover......Page 1
The Mathematica GuideBook
for Symbolics......Page 4
ISBN-13: 9780387950204......Page 5
Preface......Page 6
References......Page 14
Contents......Page 16
Introduction and Orientation to
The Mathematica GuideBooks......Page 20
1
Symbolic Computations......Page 40
1.1 Introduction......Page 41
1.2 Operations on Polynomials......Page 53
1.3 Operations on Rational Functions......Page 118
1.4 Operations on Trigonometric Expressions......Page 128
1.5 Solution of Equations......Page 134
1.6 Classical Analysis......Page 169
1.7 Differential and Difference Equations......Page 273
1.8 Integral Transforms and Generalized Functions......Page 306
1.9 Additional Symbolics Functions......Page 334
1.10 Three Applications......Page 338
2
Classical Orthogonal Polynomials......Page 842
2.1 General Properties of Orthogonal Polynomials......Page 843
2.2 Hermite Polynomials......Page 846
2.3 Jacobi Polynomials......Page 856
2.4 Gegenbauer Polynomials......Page 863
2.5 Laguerre Polynomials......Page 872
2.6 Legendre Polynomials......Page 882
2.7 Chebyshev Polynomials of the First Kind......Page 889
2.8 Chebyshev Polynomials of the Second Kind......Page 893
2.9 Relationships Among the Orthogonal Polynomials......Page 900
2.10 Ground-State of the Quartic Oscillator......Page 908
Exercises......Page 925
Solutions......Page 937
References......Page 1001
3
Classical Special Functions......Page 1018
3.0 Remarks......Page 1019
3.1 Introduction......Page 1029
3.2 Gamma, Beta, and Polygamma Functions......Page 1041
3.3 Error Functions and Fresnel Integrals......Page 1048
3.4 Exponential Integral and Related Functions......Page 1056
3.5 Bessel and Airy Functions......Page 1059
3.6 Legendre Functions......Page 1084
3.7 Hypergeometric Functions......Page 1089
3.8 Elliptic Integrals......Page 1102
3.9 Elliptic Functions......Page 1111
3.10 Product Log Function......Page 1121
3.11 Mathieu Functions......Page 1126
3.12 Additional Special Functions......Page 1149
3.13 Solution of Quintic Polynomials......Page 1150
Exercises......Page 1165
Solutions......Page 1195
References......Page 1433
Index......Page 1471