Raimundas Vidunas

Faculty of Mathematics

Kobe University

email: vidunas AT math DOT kobe-u DOT ac DOT jp
telephone: +81-78-803-5611
fax: +81-78-803-5610

Research

I am an assistant professor, employed by Organization of Advanced Science and Technology at Kobe University. My main research of interest are: Hypergeometric functions, Special functions, Leonard pairs, Non-commutative geometry, Splines.
From 2003 till 2006, I was a post-doc at Kyushu University within The 21st Century COE Program .
An earlier project was "Non-commutative geometry" (supported by ESF, EC and the Flemish FWO), at Antwerp University and at the Free University of Brussels (VUB). Here is the webpage of the Algebra and Geometry research group in Antwerp.
My 1999-2001 project was Algorithmic Methods for Special Functions by Computer Algebra , supported by the Dutch NWO.
Approaching the Rainbow (a presentation).
My PhD thesis (and here is Errata to it ).
My latest application for a JSPS grant.
Curriculum Vitae .

Latest papers

Cubic and quartic transformations of the sixth Painleve equation in terms of Riemann-Hilbert correspondence, with M. Mazzocco.
Transformations and invariants for dihedral Gauss hypergeometric functions . Accepted by Kyushu Journal of Mathematics.
Arithmetic identities characterising Heun functions reducible to hypergeometric functions , with M. van Hoiej.
A generalization of Clausen's identity . Ramanujan Journal, Vol 26 (2011), pg. 133-146.

Other papers

Gauss hypergeometric functions:
Dihedral Gauss hypergeometric functions , Kyushu Journal of Mathematics, Vol. 65 (2011), pg. 141-167.
Degenerate Gauss hypergeometric functions , Kyushu Journal of Mathematics, Vol. 61 (2007), pg. 109-135.
Darboux evaluations of algebraic Gauss hypergeometric functions, some explicit evaluations of algebraic Gauss hypergeometric functions.
A Generalization of Kummer's Identity The Rocky Mountain Journal of Mathematics, Vol. 32 (2002), pg. 919-936.
Transformations of Gauss hypergeometric functions:
General transformations between the Heun and Gauss hypergeometric functions, with Galina Filipuk.
Algebraic transformations of Gauss hypergeometric functions . Funkcialaj Ekvacioj, Vol 52 (Aug 2009), pg. 139-180.
The most general paper of the long project. Here is an earlier short version (8 pages). Check also the software list.
Transformations of some Gauss hypergeometric functions , The "hyperbolic" case. Journal of Computational and Applied Mathematics, Vol. 178 (2005), pg. 473-487.
Transformations of algebraic Gauss hypergeometric functions , computation of Klein's pullback transformations for algebraic 2F1 functions.
Transformations of hypergeometric elliptic integrals .
Hypergeometric functions in general:
Specialization of Appell's functions to univariate hypergeometric functions, Journal of Mathematical Analysis and Applications, Vol. 355 (2009), pg. 145-163.
On singular univariate specializations of bivariate hypergeometric functions , Journal of Mathematical Analysis and Applications, Vol. 365 (2010), pg. 135-141.
Uniform convergence of hypergeometric series . (For Zeilberger's method applied to non-terminating hypergeometric series.)
Contiguous relations of hypergeometric series , with corrected formulas (24)-(25) of the published text ("Journal of Computational and Applied Mathematics", Vol. 153 (2003), pg. 507-519).
Differential equations of order two with one singular point , Journal of Symbolic Computation, Vol. 28 (1999), pg. 495-520.
The Painleve equations:
Quadratic Transformations of the Sixth Painleve Equation with application to algebraic solutions, with A.V. Kitaev. Mathematische Nachrichten, Vol 280, No 16 (Dec 2007), pg. 1834-1855.
Computation of Highly Ramified Coverings, with A.V. Kitaev. Mathematics of Computation, Vol 78 (Oct 2009), pg. 2371-2395.
Computation of RS-pullback transformations for algebraic Painleve VI solutions, with A.V. Kitaev.
Schlesinger transformations for algebraic Painleve VI solutions , with A.V. Kitaev.
Asymptotics:
Parabolic cylinder functions: examples of error ounds for asymptotic expansions, with N. Temme, Analysis and Applications, Vol. 1, No. 3 (2003), pg. 265-288.
Symbolic evaluation of coefficients in Airy-type asymptotic expansions, with N. Temme, Journal of Mathematical Analysis and Applications, Vol. 269 (2002), pg. 317-331.
Leonard pairs:
Askey-Wilson relations and Leonard pairs. Discrete Mathematics, Volume 308, Issue 4 (2008), pg. 479-495.
Normalized Leonard pairs and Askey-Wilson relations. Linear Algebra and its Applications, Vol. 422 (2007), pg. 39-57.
Leonard pairs and the Askey-Wilson relations, with Paul Terwilliger. "Journal of Algebra and Its Applications", Vol. 3, No. 4 (2004), pg. 411-426.
Simultaneously lowering operators, RIMS Kokyoryoku No 1593, "Finite Groups and Algebraic Combinatorics" (2008), pg. 78-86.
Other:
Expressions for values of the gamma function , Kyushu Journal of Mathematics, Vol. 59 (2005), pg. 267-283. With explicit relations of gamma values at rational points with the denominator dividing 24 or 60. See also developed scientific software (here below).
Geometrically continuous octahedron, in R.Goldman, R.Krasauskas (Ed.), "Topics in Algebraic Geometry and Geometric Modeling", AMS series "Contemporary Mathematics" #334 (2003).
A linear algebra exercise , with F. Beukers, R. van Luijk. Nieuw Archief voor Wiskunde V-3, June 2002, pg. 42-43. This is arithmetic geometry really.
A greatest common divisor algorithm , with A. Belenkyi. International Journal of Algebra and Computation, Vol. 8, No 5 (1998), pg. 617-623. Something like the half-GCD algorithm.
Detecting persistent regimes in the North Atlantic Oscillation time series. Some analysis of climate data.

Developed scientific software

(Use Maple's commando "read", or Mathematica's commando "<<" to load the packages.)

A Maple package gammas120.mpl , and a Mathematica package gammas120.m , for simplification of expressions with gamma values at rational points with the denominator dividing 120.
A Maple worksheet summarising algebraic transformations of Gauss hypergeometric functions. A supplementary service package should be loaded (into the same directory) as well.
A Maple package infhsum.mpl for summation of non-terminating hypergeometric series by an extension of Zeilberger's method.
Here is an accompanying Maple worksheet. I use W. Koepf's package hsum6.mpl .
A Maple package contiguous2f1.mpl for computing contiguous relations of Gauss hypergeometric functions. Here is an accompanying Maple worksheet (with material added by T.H. Koornwinder).
A Maple package airypcf.mpl for computing coefficients in Airy-type asymptotic expansions (see this paper). And here is an accompanying Maple worksheet.

Links

Last modified: Monday, October 24, 2011