On the coefficients of differentiated expansions of ultraspherical polynomials
Applied Numerical Mathematics
Inverting polynomials and formal power series
SIAM Journal on Computing
Computing expansion coefficients in orthogonal bases of ultraspherical polynomials
Journal of Computational and Applied Mathematics
Algorithm 757: MISCFUN, a software package to compute uncommon special functions
ACM Transactions on Mathematical Software (TOMS)
Methods for Fitting Rational Approximations, Part I: Telescoping Procedures for Continued Fractions
Journal of the ACM (JACM)
Closed-form expressions for certain induction integrals involving Jacobi and Chebyshev polynomials
Journal of Computational Physics
Algorithm: ten subroutines for the manipulation of Chebyshev series
Communications of the ACM
Construction of rational and negative powers of a formal series
Communications of the ACM
Algorithm 277: Computation of Chebyshev series coefficients
Communications of the ACM
Automation and Remote Control
Some error expansions for certain Gaussian quadrature rules
Journal of Computational and Applied Mathematics
A quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight-function
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Hi-index | 7.29 |
The Chebyshev series expansion Σn=0∞anTn(x) of the inverse of a polynomial Σj=0kbjTj(x) is well defined if the polynomial has no roots in [-1,1]. If the inverse polynomial is decomposed into partial fractions, the an are linear combinations of simple functions of the polynomial roots. Also, if the first k of the coefficients an are known, the others become linear combinations of these derived recursively from the bj's. On a closely related theme, finding a polynomial with minimum relative error towards a given f(x) is approximately equivalent to finding the bj in f(x)/Σ0k bj Tj(x) = 1 + Σk+1∞ an Tn(x); a Newton algorithm produces these if the Chebyshev expansion of f(x) is known.