A permutations representation that knows what “Eulerian” means.
A study of Eulerian numbers for permutations in the alternating group.
A study on the -adic integral representation on associated with Bernstein and Bernoulli polynomials.
A study on the -adic -integral representation on associated with the weighted -Bernstein and -Bernoulli polynomials.
A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function
We study the interplay between recurrences for zeta related functions at integer values, 'Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and Grosswald, the transcendence of the zeta function at odd integer values, the Li Criterion for the Riemann Hypothesis and pseudo-characteristic polynomials for zeta related functions. We begin with a recent result for ζ(2s) and some seemingly new Bernoulli relations,...
Advanced determinant calculus.
Algorithms for Bernoulli and related polynomials.
Algorithms for Bernoulli numbers and Euler numbers.
An Alternative Form of the Functional Equation for Riemann’s Zeta Function, II
This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for . We present here, after showing the first proof of Riemann, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta function and the alternating Zeta function, connected with odd numbers. A proof that Euler himself could have arranged with a little step at the end of his paper “Remarques sur un beau rapport entre...
An asymptotic expansion for the Bernoulli numbers of the second kind.
An extension of a theorem of Nielsen
An extension of -zeta function.
An infinite family of dual sequence identities.
Applications de la dérivation d'Arbogast à la solution de la partition des nombres et à d'autres problèmes
Approximate counting via Euler transform
Arithmetic Properties of Generalized Bernoulli Numbers.
Arithmetic theory of harmonic numbers (II)
For k = 1,2,... let denote the harmonic number . In this paper we establish some new congruences involving harmonic numbers. For example, we show that for any prime p > 3 we have , , and for any positive integer n < (p-1)/6, where B₀,B₁,B₂,... are Bernoulli numbers, and .
Asymptotics for Lacunary sums of binomial coefficients and a card problem with ranks.
Asymptotische Entwicklung von verallgemeinerten Bernoullischen Funktionen und von Teilsummen Dirichletscher Reihen mit periodischer Koeffizientenfolge.
Beiträge zu der Kenntniss der Bernouillischen Zahlen.