The publications and software of Raimundas Vidunas

Heun functions, Belyi maps

• Belyi functions for hyperbolic hypergeometric-to-Heun transformations, with M. van Hoeij.
• Algorithms and differential relations for Belyi functions, with M. van Hoeij.
• Arithmetic identities characterising Heun functions reducible to hypergeometric functions , with M. van Hoiej.
• A Maple routine for computing genus 0 Belyi functions, supplementing the work with M. van Hoeij.
  
  
• Degenerate and dihedral Heun functions with parameters. Accepted by Hokkaido Journal of Mathematics.
• A classification of coverings yielding Heun-to-hypergeometric reductions, with G. Filipuk. To appear in Osaka Journal of Mathematics.
• Parametric transformations between the Heun and Gauss hypergeometric functions, with G. Filipuk. Funkcialaj Ekvacioj, Vol. 56 (2013), pg 271-321.
• A Maple package for computing identities between Heun and hypergeometric functions in the papers with G. Filipuk.

Hypergeometric functions and their transformations

• Darboux evaluations of algebraic Gauss hypergeometric functions, Kyushu Journal of Mathematics, Vol. 67 (2013), pg. 239-280.
• Transformations and invariants for dihedral Gauss hypergeometric functions . Kyushu Journal of Mathematics, Vol. 66 (2012), pg. 143-170.
• 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.
• A generalization of Kummer's identity The Rocky Mountain Journal of Mathematics, Vol. 32 (2002), pg. 919-936.
  
  
• 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).
• 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 .
• A Maple worksheet summarising algebraic transformations of Gauss hypergeometric functions. A supplementary service package should be loaded (into the same directory) as well.
  
  
• A generalization of Clausen's identity . Ramanujan Journal, Vol 26 (2011), pg. 133-146.
• 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 in "Journal of Computational and Applied Mathematics", Vol. 153 (2003), pg. 507-519.
• 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).

Painleve functions

• Cubic and quartic transformations of the sixth Painleve equation in terms of Riemann-Hilbert correspondence, with M. Mazzocco. Studies in Applied Mathematics, Vol. 130 (2013), pg. 17-48.
• A Maple worksheet for computing 2x2 gauge transformations corresponding to the Painleve VI transformations in the work with M. Mazzocco.
  
  
• Computation of Highly Ramified Coverings, with A.V. Kitaev. Mathematics of Computation, Vol 78 (Oct 2009), pg. 2371-2395.
• 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 RS-pullback transformations for algebraic Painleve VI solutions, with A.V. Kitaev.
• Schlesinger transformations for algebraic Painleve VI solutions , with A.V. Kitaev.

Other special functions

• 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.
• 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.
  (Use Maple's commando "read", or Mathematica's commando "<<" to load the packages.)
  
  
• Differential equations of order two with one singular point , Journal of Symbolic Computation, Vol. 28 (1999), pg. 495-520.
• Parabolic cylinder functions: examples of error bounds 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.
• A Maple package airypcf.mpl for computing coefficients in Airy-type asymptotic expansions, with an accompanying Maple worksheet.

Leonard pairs

• Askey-Wilson relations and Leonard pairs. Discrete Mathematics, Vol. 308, No 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 publications

• 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. Belenkiy. 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.

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