4 citations · 10 across the 25 of their papers we have counts for
5 papers · 1 filter
New trigonometric identities and reciprocity laws of generalized Dedekind sums II
Genki Shibukawa
We obtain new trigonometric identities, which are product-to-sum type formulas for derivative of the cosecant and cotangent functions. Further, from specializations of our formulas…
Bilateral zeta functions associated with the multiple sine functions
Genki Shibukawa
We introduce two types bilateral zeta functions, which are related to the primitive and normalized multiple sine functions respectively. Further, we establish their main properties…
New trigonometric identities and reciprocity laws of generalized Dedekind sums
Genki Shibukawa
We obtain new trigonometric identities, which are some product-to-sum type formulas for the higher derivative of the cotangent and cosecant functions. Further, from specializations…
Multivariate circular Jacobi polynomials
Genki Shibukawa
We introduce a new multivariate orthogonal polynomial which is a 2-parameter deformation of the spherical polynomial by harmonic analysis on symmetric cone. This is also regarded a…
Multivariate Meixner, Charlier and Krawtchouk polynomials
Genki Shibukawa
We introduce some multivariate analogues of Meixner, Charlier and Krawtchouk polynomials, and establish their main properties, that is, duality, degenerate limits, generating funct…