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Hankel Determinants of shifted sequences of Bernoulli and Euler numbers
Karl Dilcher, Lin Jiu
Hankel determinants of sequences related to Bernoulli and Euler numbers have been studied before, and numerous identities are known. However, when a sequence is shifted by one unit…
On a result of Koecher concerning Markov-Apéry type formulas for the Riemann zeta function
Karl Dilcher, Christophe Vignat
Koecher in 1980 derived a method for obtaining identities for the Riemann zeta function at odd positive integers, including a classical result for due to Markov and rediscov…
Hankel Determinants of sequences related to Bernoulli and Euler Polynomials
Karl Dilcher, Lin Jiu
We evaluate the Hankel determinants of various sequences related to Bernoulli and Euler numbers and special values of the corresponding polynomials. Some of these results arise as…
Orthogonal polynomials and Hankel Determinants for certain Bernoulli and Euler Polynomials
Karl Dilcher, Lin Jiu
Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials …
Arithmetic properties of polynomial solutions of the Diophantine equation
Karl Dilcher, Maciej Ulas
For each integer we consider the unique polynomials of smallest degree that are solutions of the equation . We d…
Polynomial analogues of restricted multicolor b-ary partition functions
Karl Dilcher, Larry Ericksen
Given an integer base , a number of colors, and a finite sequence of positive integers, we introduce the concept of a -restricted -col…