4 citations · 10 across the 25 of their papers we have counts for
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The generalized Zwegers' -function and transformation formulas for the bilateral basic hypergeometric series
Genki Shibukawa, Satoshi Tsuchimi
By applying Slater's transformation formulas for the bilateral basic hypergeometric series , we derive three type translation formulas for the generalized Zwegers' -f…
A Generalization of Zwegers' -Function According to the -Hermite-Weber Difference Equation
Genki Shibukawa, Satoshi Tsuchimi
We introduce a one parameter deformation of the Zwegers' -function as the image of -Borel and -Laplace transformations of a fundamental solution for the -Hermite-Weber…
New Pieri Type Formulas for Jack Polynomials and their Applications to Interpolation Jack Polynomials
Genki Shibukawa
We present new Pieri type formulas for Jack polynomials. As an application, we give a new derivation of higher order difference equations for interpolation Jack polynomials origina…
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…
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…
Bilateral zeta functions and their applications
Genki Shibukawa
We introduce a new type of multiple zeta functions, which we call bilateral zeta functions, analogous to the Barnes zeta functions. The bilateral zeta function is a periodic functi…