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On the coefficients of differentiated expansions of ultraspherical polynomials. (English) Zbl 0748.65063
The authors prove formulae associated with the differentiation of expansions of ultraspherical polynomials and describe how they can be used to solve two-point boundary value problems. Formulae relating the coefficients in expansions which have been differentiated an arbitrary number of times to those in the original expansion are proved. Particular expressions for the Chebyshev and Legendre polynomials are derived.
Reviewer: K.Najzar (Praha)

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65D20 Computation of special functions and constants, construction of tables
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
33C55 Spherical harmonics
34B05 Linear boundary value problems for ordinary differential equations
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