The HolonomicFunctions package by Christoph Koutschan allows to deal with multivariate holonomic functions and sequences in an algorithmic fashion. For this purpose the package can compute annihilating ideals and execute closure properties (addition, multiplication, substitutions) for such functions. An annihilating ideal represents the set of linear differential equations, linear recurrences, q-difference equations, and mixed linear equations that a given function satisfies. Summation and integration of multivariate holonomic functions can be performed via creative telescoping. As subtasks, the following functionalities have been implemented in HolonomicFunctions: computations in Ore algebras (noncommutative polynomial arithmetic with mixed difference-differential operators), noncommutative Gröbner bases, and solving of coupled linear systems of differential or difference equations.

References in zbMATH (referenced in 50 articles , 2 standard articles )

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  1. Görlach, Paul; Lehn, Christian; Sattelberger, Anna-Laura: Algebraic analysis of the hypergeometric function (_1F_1) of a matrix argument (2021)
  2. Paule, Peter; Radu, Cristian-Silviu: Holonomic relations for modular functions and forms: first guess, then prove (2021)
  3. Wiart, Jaspar; Wong, Elaine: Walsh functions, scrambled (( 0 , m , s ))-nets, and negative covariance: applying symbolic computation to quasi-Monte Carlo integration (2021)
  4. Cai, Fangfang; Hou, Qing-Hu; Sun, Yidong; Yang, Arthur L. B.: Combinatorial identities related to (2 \times2) submatrices of recursive matrices (2020)
  5. Cluzeau, Thomas; Koutschan, Christoph; Quadrat, Alban; Tõnso, Maris: Effective algebraic analysis approach to linear systems over Ore algebras (2020)
  6. Hoffmann, Johannes; Levandovskyy, Viktor: Constructive arithmetics in Ore localizations of domains (2020)
  7. Jiu, Lin; Koutschan, Christoph: Calculation and properties of zonal polynomials (2020)
  8. Quadrat, Alban (ed.); Zerz, Eva (ed.): Algebraic and symbolic computation methods in dynamical systems. Based on articles written for the invited sessions of the 5th symposium on system structure and control, IFAC, Grenoble, France, February 4--6, 2013 and of the 21st international symposium on mathematical theory of networks and systems (MTNS 2014), Groningen, the Netherlands, July 7--11, 2014 (2020)
  9. Takayama, Nobuki; Jiu, Lin; Kuriki, Satoshi; Zhang, Yi: Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix (2020)
  10. Blümlein, J.; De Freitas, A.; Raab, C. G.; Schönwald, K.: The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering (2019)
  11. Blümlein, J.; Raab, C.; Schönwald, K.: The polarized two-loop massive pure singlet Wilson coefficient for deep-inelastic scattering (2019)
  12. Chen, Shaoshi; Kauers, Manuel; Li, Ziming; Zhang, Yi: Apparent singularities of D-finite systems (2019)
  13. Koutschan, Christoph; Thanatipanonda, Thotsaporn: A curious family of binomial determinants that count rhombus tilings of a holey hexagon (2019)
  14. Blümlein, Johannes; Round, Mark; Schneider, Carsten: Refined holonomic summation algorithms in particle physics (2018)
  15. Chen, Herman Z. Q.; Yang, Arthur L. B.; Zhang, Philip B.: The real-rootedness of generalized Narayana polynomials related to the Boros-Moll polynomials (2018)
  16. Koutschan, Christoph; Paule, Peter: Holonomic tools for basic hypergeometric functions (2018)
  17. Koutschan, Christoph; Zhang, Yi: Desingularization in the (q)-Weyl algebra (2018)
  18. Shalosh B. Ekhad, Doron Zeilberger: How Many Rounds Should You Expect in Urn Solitaire? (2018) arXiv
  19. Hoffmann, Johannes; Levandovskyy, Viktor: A constructive approach to arithmetics in Ore localizations (2017)
  20. Johannes Hoffmann, Viktor Levandovskyy: Constructive Arithmetics in Ore Localizations of Domains (2017) arXiv

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Further publications can be found at: http://www.risc.jku.at/publications/