Algorithms for the integration and derivation of Chebyshev series

摘要

General formulas for the mth integral and derivative of a Chebyshev polynomial of the first or second kind are presented. The result is expressed as a finite series of the same kind of Chebyshev polynomials. These formulas permit to accelerate the determination of such integrals or derivatives. Besides, it is presented formulas for the mth integral and derivative of finite Chebyshev series and a numerical algorithm for the direct evaluation of the mth derivative of such a series.