4 citations · 10 across the 25 of their papers we have counts for
4 papers · 1 filter
New identities for some symmetric polynomials, and a higher order analogue of the Fibonacci and Lucas numbers
Genki Shibukawa
We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.
Multivariate Bernoulli polynomials
Genki Shibukawa
We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties: difference and differential relations, symmetry, explicit formula, inversion fo…
An elliptic analogue of Fukuhara's trigonometeric identities
Genki Shibukawa
We obtain new elliptic function identities, which are an elliptic analogue of Fukuhara's trigonometric identities. We show that the coefficients of Laurent expansions at of o…
Some arithmetic properties of an elliptic Dedekind sum
Genki Shibukawa
We give an explicit expression of the elliptic classical Dedekind sum which is a special case of multiple elliptic Dedekind sums introduced by Egami. We also determine the denomina…