Untitled - Cdm.unimo.it

CONTENTS
1. Special families of polynomials
1.1 Sturm-Liouville problems 1
1.2 The Gamma function 2
1.3 Jacobi polynomials 4
1.4 Legendre polynomials 7
1.5 Chebyshev polynomials 9
1.6 Laguerre polynomials 12
1.7 Hermite polynomials 16
2. Orthogonality
2.1 Inner products and norms 21
2.2 Orthogonal functions 23
2.3 Fourier coefficients 27
2.4 The projection operator 30
2.5 The maximum norm 31
2.6 Basis transformations 32
3. Numerical integration
3.1 Zeroes of orthogonal polynomials 35
3.2 Lagrange polynomials 42
3.3 The interpolation operators 46