Phillips, Timothy N. On the Legendre coefficients of a general-order derivative of an infinitely differentiable function. (English) Zbl 0667.42011 IMA J. Numer. Anal. 8, No. 4, 455-459 (1988). An explicit formula is derived which relates the Legendre coefficients \(a_ n^{(q)}\) of the derivative \(f^{(q)}(x)\), \(q=1,2,..\). with a sum of the Legendre coefficients \(a_ n=a_ n^{(0)}\) of a function f(x). Reviewer: J.B.Butler jun Cited in 21 Documents MSC: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 65L15 Numerical solution of eigenvalue problems involving ordinary differential equations Keywords:Legendre coefficients PDFBibTeX XMLCite \textit{T. N. Phillips}, IMA J. Numer. Anal. 8, No. 4, 455--459 (1988; Zbl 0667.42011) Full Text: DOI