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A method is given to find a recurrence relation for the coefficients of the series expansion of a function f with respect to classical orthogonal polynomials of a discrete variable, which follows from a linear difference equation satisfied by f.

Recurrence relations with periodic coefficients and Chebyshev polynomials

Bernhard Beckermann, Jacek Gilewicz, Elie Leopold (1995)

Applicationes Mathematicae

We show that polynomials defined by recurrence relations with periodic coefficients may be represented with the help of Chebyshev polynomials of the second kind.

Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials

Stanislaw Lewanowicz (2002)

Applicationes Mathematicae

Let $P_{k}$ be any sequence of classical orthogonal polynomials. Further, let f be a function satisfying a linear differential equation with polynomial coefficients. We give an algorithm to construct, in a compact form, a recurrence relation satisfied by the coefficients $a_{k}$ in $f = \sum_{k} a_{k} P_{k}$ . A systematic use of the basic properties (including some nonstandard ones) of the polynomials $P_{k}$ results in obtaining a low order of the recurrence.

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Radial solutions to a superlinear Dirichlet problem using Bessel functions.

Radicals and units in Ramanujan's work

Raising and lowering operators for Askey-Wilson polynomials.

Ramanujan type trigonometric formulas: the general form for the argument $\frac{2 π}{7}$ .

Ramanujan's class invariants and cubic continued fraction

Ramanujan's entries and solutions of incomplete elliptic integrals in terms of hypergeometric functions.

Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions

Ratio monotonicity of polynomials derived from nondecreasing sequences.

Rational solutions of the Sasano system of type $A_{5}^{(2)}$ .

Recherches sur les fonctions cylindriques et le développement des fonctions continues en séries

Recherches sur quelques produits indéfinis et sur la constante G (Complément).

Recurrence formulae for multi-poly-Bernoulli numbers.

Recurrence Formulas for Zonal Polynomials.

Recurrence relation for a class of polynomials associated with the generalized Hermite polynomials.

Recurrence relations for the coefficients of expansions in classical orthogonal polynomials of a discrete variable

Recurrence relations with periodic coefficients and Chebyshev polynomials

Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials

Recursive computation of certain integrals of elliptic type.

Redheffer type inequality for Bessel functions.

Reduction of Certain Generalized Kampé de Fériet Functions.

Currently displaying 1 – 20 of 53