Expansions in series of Chebyshev polynomials of a function occuring in linear unsteady aerodynamic theory

Abstract

A procedure is described for obtaining expansions in series of Chebyshev polynomials of the function [integration of e(to the minus i alpha u)du/(u squared plus 1) to the power of n + half] for all real alpha and all integer n >= 0 . Numerical values are given of the coefficients of the series of Chebyshev polynomials obtained from a FORTRAN program. The leading coefficients are given to twelve significant decimal digits.