Research Article
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Year 2021, , 81 - 90, 01.03.2021
https://doi.org/10.33205/cma.810478

Abstract

References

  • U. Abel, G. Arends: A remark on some combinatorial identities, General Mathematics, 26 (1–2) (2018), 35-40.
  • A. E. Bârar: Some families of rational Heun functions and combinatorial identities, General Mathematics, 25 (1-2)(2017), 29–36.
  • A. Bârar, G. Mocanu and I. Raşa: Bounds for some entropies and special functions, Carpathian Journal of Mathematics, 34 (1) (2018), 9-15.
  • A. Bârar, G. Mocanu and I. Raşa: Heun functions related to entropies, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 113 (2019), 819–830.
  • H. W. Gould: Combinatorial identities, Morgantown, W. Va. (1972).
  • M. Hortaçsu: Heun Functions and Some of Their Applications in Physics, Advances in High Energy Physics, (8621573), (2018), 14 pages.
  • A. Ishkhanyan, K. A. Suominen: New solutions of Heun’s general equation, Journal of Physics A: Mathematical and General, 36 (2003), L81-L85.
  • R. S. Maier: The 192 solutions of the Heun equation, Mathematics and Computation, 76 (2007), 811-843.
  • R. S. Maier: On reducing the Heun equation to the hypergeometric equation, Journal of Differential Equations, 213 (2005), 171-203.
  • Gh. Mocicâ: Probleme de func¸tii speciale, Editura Didacticâ¸si Pedagogicâ, Bucure¸sti (1998).
  • NIST Digital library of Mathematical Functions, http://dlmf.nist.gov.
  • I. Raşa: Rényi entropy and Tsallis entropy associated with positive linear operators, arXiv:1412.4971v1 [math.CA] (2014).
  • I. Raşa: Entropies and the derivatives of some Heun functions, arXiv: 1502.05570 (2015).
  • I. Raşa: Entropies and Heun functions associated with positive linear operators, Applied Mathematics and Computation, 268 (2015), 422-431.
  • A. Ronveaux: Heun’s Differential Equations, London: Oxford University Press (1995).
  • V. A. Shahnazaryan, T. A. Ishkhanyan, T. A. Shahverdyan and A. M. Ishkhanyan: New relations for the derivative of the confluent Heun function, Armenian Journal of Physics, 5 (2012), 146-156.

Heun equations and combinatorial identities

Year 2021, , 81 - 90, 01.03.2021
https://doi.org/10.33205/cma.810478

Abstract

Heun functions are important for many applications in
Mathematics, Physics and in thus in interdisciplinary phenomena modelling. They satisfy second order differential
equations and are usually represented by power series. Closed forms and
simpler polynomial representations are useful. Therefore, we study and derive closed forms for
several families of Heun functions related to classical entropies. By
comparing two expressions of the same Heun function, we get several
combinatorial identities generalizing some classical ones.

References

  • U. Abel, G. Arends: A remark on some combinatorial identities, General Mathematics, 26 (1–2) (2018), 35-40.
  • A. E. Bârar: Some families of rational Heun functions and combinatorial identities, General Mathematics, 25 (1-2)(2017), 29–36.
  • A. Bârar, G. Mocanu and I. Raşa: Bounds for some entropies and special functions, Carpathian Journal of Mathematics, 34 (1) (2018), 9-15.
  • A. Bârar, G. Mocanu and I. Raşa: Heun functions related to entropies, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 113 (2019), 819–830.
  • H. W. Gould: Combinatorial identities, Morgantown, W. Va. (1972).
  • M. Hortaçsu: Heun Functions and Some of Their Applications in Physics, Advances in High Energy Physics, (8621573), (2018), 14 pages.
  • A. Ishkhanyan, K. A. Suominen: New solutions of Heun’s general equation, Journal of Physics A: Mathematical and General, 36 (2003), L81-L85.
  • R. S. Maier: The 192 solutions of the Heun equation, Mathematics and Computation, 76 (2007), 811-843.
  • R. S. Maier: On reducing the Heun equation to the hypergeometric equation, Journal of Differential Equations, 213 (2005), 171-203.
  • Gh. Mocicâ: Probleme de func¸tii speciale, Editura Didacticâ¸si Pedagogicâ, Bucure¸sti (1998).
  • NIST Digital library of Mathematical Functions, http://dlmf.nist.gov.
  • I. Raşa: Rényi entropy and Tsallis entropy associated with positive linear operators, arXiv:1412.4971v1 [math.CA] (2014).
  • I. Raşa: Entropies and the derivatives of some Heun functions, arXiv: 1502.05570 (2015).
  • I. Raşa: Entropies and Heun functions associated with positive linear operators, Applied Mathematics and Computation, 268 (2015), 422-431.
  • A. Ronveaux: Heun’s Differential Equations, London: Oxford University Press (1995).
  • V. A. Shahnazaryan, T. A. Ishkhanyan, T. A. Shahverdyan and A. M. Ishkhanyan: New relations for the derivative of the confluent Heun function, Armenian Journal of Physics, 5 (2012), 146-156.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Adina Barar This is me 0000-0003-3659-2987

Gabriela Mocanu 0000-0002-1934-4618

Ioan Raşa 0000-0002-5206-030X

Publication Date March 1, 2021
Published in Issue Year 2021

Cite

APA Barar, A., Mocanu, G., & Raşa, I. (2021). Heun equations and combinatorial identities. Constructive Mathematical Analysis, 4(1), 81-90. https://doi.org/10.33205/cma.810478
AMA Barar A, Mocanu G, Raşa I. Heun equations and combinatorial identities. CMA. March 2021;4(1):81-90. doi:10.33205/cma.810478
Chicago Barar, Adina, Gabriela Mocanu, and Ioan Raşa. “Heun Equations and Combinatorial Identities”. Constructive Mathematical Analysis 4, no. 1 (March 2021): 81-90. https://doi.org/10.33205/cma.810478.
EndNote Barar A, Mocanu G, Raşa I (March 1, 2021) Heun equations and combinatorial identities. Constructive Mathematical Analysis 4 1 81–90.
IEEE A. Barar, G. Mocanu, and I. Raşa, “Heun equations and combinatorial identities”, CMA, vol. 4, no. 1, pp. 81–90, 2021, doi: 10.33205/cma.810478.
ISNAD Barar, Adina et al. “Heun Equations and Combinatorial Identities”. Constructive Mathematical Analysis 4/1 (March 2021), 81-90. https://doi.org/10.33205/cma.810478.
JAMA Barar A, Mocanu G, Raşa I. Heun equations and combinatorial identities. CMA. 2021;4:81–90.
MLA Barar, Adina et al. “Heun Equations and Combinatorial Identities”. Constructive Mathematical Analysis, vol. 4, no. 1, 2021, pp. 81-90, doi:10.33205/cma.810478.
Vancouver Barar A, Mocanu G, Raşa I. Heun equations and combinatorial identities. CMA. 2021;4(1):81-90.