| MSC: | 11A63 | Radix representation; digital problems |
| 39A10 | Difference equations, additive | |
| 11B68 | Bernoulli and Euler numbers and polynomials | |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
Abstract:
This paper is a direct continuation of [*] concerning the representation of
power sums related to digital sequences. Foundation is beside article [*] an existence theorem
for differentiable solutions of certain two-scale difference equations with a parameter.
By means of such solutions and a method developed in [*] we are able to give an explicit
representation for general sums related to digital sequences. In particular, we give a summation
formula for power sums of the sum of digits and incidentally, we find a new property
of the Bernoulli polynomials.
[*]Krüppel, M. : Two-scale difference equations and power sums related to digital sequences.
Rostock. Math. Kolloq. 68, 45 - 64 (2013)