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On the Legendre coefficients of a general-order derivative of an infinitely differentiable function. (English) Zbl 0667.42011

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

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
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