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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.

Récurrences $2$ - et $3$ -mahlériennes

Bernard Randé (1993)

Journal de théorie des nombres de Bordeaux

On sait (Cobham) qu’une suite $2$ - et $3$ -automatique est une suite rationnelle. Une question de Loxton et van der Poorten étend ce résultat au cas $2$ - et $3$ -régulier. On montre dans cet article que, si une suite vérifie une récurrence $2$ - et $3$ -mahlérienne d’ordre un, elle est rationnelle.

Recursive inset entropies of multiplicative type on open domains.

Pl. Kannappan, B.R. Ebanks, C.T. Ng (1988)

Aequationes mathematicae

Reducibility and stability results for linear system of difference equations.

Tiryaki, Aydin, Misir, Adil (2008)

Advances in Difference Equations [electronic only]

Reducible Linear Difference Operators

CHARLES H. FRANKE (1973)

Aequationes mathematicae

Reduction of the modified Poincaré differential equation to Birkhoff matrix form.

Risteski, Ice B. (1999)

Southwest Journal of Pure and Applied Mathematics [electronic only]

Refinement type equations: sources and results

Rafał Kapica, Janusz Morawiec (2013)

Banach Center Publications

It has been proved recently that the two-direction refinement equation of the form $f (x) = \sum_{n \in} c_{n, 1} f (k x - n) + \sum_{n \in ℤ} c_{n, - 1} f (- k x - n)$ can be used in wavelet theory for constructing two-direction wavelets, biorthogonal wavelets, wavelet packages, wavelet frames and others. The two-direction refinement equation generalizes the classical refinement equation $f (x) = \sum_{n \in ℤ} c ₙ f (k x - n)$ , which has been used in many areas of mathematics with important applications. The following continuous extension of the classical refinement equation $f (x) = \int_{ℝ} c (y) f (k x - y) d y$ has also various interesting applications....

Regular fractional iteration of convex functions

Marek Kuczma (1980)

Annales Polonici Mathematici

The existence of a unique $C^{1}$ solution φ of equation (1) is proved under the condition that f: I → I is convex or concave and of class $C^{1}$ in I, 0 < f(x) < x in I*, and f’(x) > 0 in I. Here I = [0, a] or [0, a), 0 < a ≤ ∞, and I* = I 0.

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R-and T-Groupoids: A Generalization of Groups.

Random stability of an additive-quadratic-quartic functional equation.

Rank of matrices and the Pexider equation.

Rate of convergence of solutions of rational difference equation of second order.

Rational recursive equations characterizing cotangent-tangent and hyperbolic cotangent-tangent functions.

Recent results concerning dynamic equations on time scales.

Recent results on the stability of the parametric fundamental equation of information.

Recent trends in differential and difference equations.

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

Récurrences $2$ - et $3$ -mahlériennes

Recursive inset entropies of multiplicative type on open domains.

Reducibility and stability results for linear system of difference equations.

Reducible Linear Difference Operators

Reduction of the modified Poincaré differential equation to Birkhoff matrix form.

Refinement type equations: sources and results

Regular fractional iteration of convex functions

Regular fractional iterations.

Regular hexagons in normed spaces and a theorem of Walter Benz.

Regular Iteration in the Case of Multiplier Zero

Regularity of Refinable Functions Vectors.

Currently displaying 1 – 20 of 72