Manfred Krüppel

Two-Scale Difference Equations and Power Sums related to Digital Sequences

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 68, 45 - 64 (2013)

MSC: 39A13   Difference equations, scaling ($q$-differences) [See also 33Dxx]
  11A63   Radix representation; digital problems {For metric results, see 11K16}
  11B68   Bernoulli and Euler numbers and polynomials
  26A30   Singular functions, Cantor functions, functions with other special properties

Abstract:   This paper uncovers a connection between two-scale difference equations and the representation of sums of sequences which satisfy a certain multiplicative recurrence formula. For certain digital power sums related with such a sequence we derive a formula which in case of usual power sums yields the known representation of power sums by means of Bernoulli polynomials.

Keywords:   Two-scale difference equations, digital sums, Bernoulli polynomials, Appell polynomials, generating functions
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