Genki SHIBUKAWA

Genki SHIBUKAWA

Department of Mathematics,
Graduate School of Science, Kobe University
Division : Applied Mathematics
Assistant Professor		 Building B, Room 315

Research Field : Special Functions (SF, Sukoshi Fushigi) and their applications
Research Summary : We have studied special functions and their applications to various fields and problems (integrable systems, number theory, mathematical physics, statistics, etc.). Recently, we mainly study various formulas and special values of multivariable special functions like symmetric functions.
Primary Publications :
  1. G. Shibukawa, Operator orderings and Meixner-Pollaczek polynomials, Journal of Mathematical Physics, 54 (2013), page 4, DOI:10.1063/1.4795713.
  2. G. Shibukawa, Bilateral zeta functions and their applications, Kyushu Journal of Mathematics, 67-2 (2013), pp429--451. https://doi.org/10.2206/kyushujm.67.429
  3. T. Komatsu and G. Shibukawa, Poly-Cauchy polynomials and generalized Bernoulli polynomials, Acta Sci Math., 80 (2014), pp373--388. DOI: 10.14232/actasm-013-761-9
  4. G. Shibukawa, Multivariate Meixner, Charlier and Krawtchouk polynomials according to analysis on symmetric cones, Journal of Lie Theory, 26 (2016), pp439--477. https://www.heldermann.de/JLT/JLT26/JLT262/jlt26020.htm
  5. G. Shibukawa, New trigonometric identities and reciprocity laws of generalized Dedekind sums, Tokyo Journal of Math., 39-2 (2016), pp329--349. DOI: 10.3836/tjm/1484903126
  6. G. Shibukawa, Multivariate circular Jacobi polynomials, Josai Mathematical Monographs, 10 (2017), pp45--79. doi/10.20566/13447777_10_45
  7. G. Shibukawa, An elliptic analogue of Fukuhara's trigonometeric identities, Int. J. Math. Comput. Sci., 15-2 (2020), pp745--768.
  8. G. Shibukawa, Multivariate Bernoulli polynomials, Josai Mathematical Monographs, 12 (2020), pp187--209. doi/10.20566/13447777_12_187
  9. G. Shibukawa, Some arithmetic properties of the elliptic Dedekind sums, Journal of Algebra, Number Theory & Applications, 46-2 (2020), pp35--54.
  10. G. Shibukawa, Rational values of powers of trigonometric functions, J. Math. Tokushima Univ. 54, (2020) pp13--18.
  11. G. Shibukawa, New Pieri type formulas for Jack polynomials and their applications to interpolation Jack polynomials, SIGMA, 16 (2020) pp11.
  12. G. Shibukawa, New identities for some symmetric polynomials and a higher order analogue of the Fibonacci and Lucas numbers, Fibonacci Quart., 58-5, (2020) pp200--221.
  13. G. Shibukawa, A revisit to periodic continuants, Josai Mathematical Monographs, 13 (2021), pp3--17. doi/10.20566/13447777_13_3
  14. G. Shibukawa, Higher order difference equations for interpolation Jack polynomials, RIMS Kokyuroku Bessatsu B87 (2021) pp7--26.