Research Article
BibTex RIS Cite
Year 2018, Volume: 5 Issue: 3, 137 - 142, 08.10.2018
https://doi.org/10.13069/jacodesmath.451218

Abstract

References

  • [1] G. E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison–Wesley Publishing Co., Reading, Mass.–London–Amsterdam, 1976.
  • [2] G. E. Andrews, A. Knopfmacher, P. Paule, H. Prodinger, q–Engel series expansions and Slater’s identities, Quaest. Math. 24(3) (2001) 403–416.
  • [3] G. E. Andrews, A. Knopfmacher, P. Paule, An infinite family of Engel expansions of Rogers– Ramanujan type, Adv. Appl. Math. 25(1) (2000) 2–11.
  • [4] G. E. Andrews, J. P. O. Santos, Rogers–Ramanujan type identities for partitions with attached odd parts, Ramanujan J. 1(1) (1997) 91–99.
  • [5] B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer–Verlag, New York, 1991.
  • [6] B. C. Berndt, S. S. Huang, J. Sohn, S. H. Son, Some theorems on the Rogers–Ramanujan continued fraction in Ramanujan’s lost notebook, Trans. Amer. Math. Soc. 352 (2000) 2157–2177.
  • [7] D. M. Bressoud, Some identities for terminating q-series, Math. Proc. Cambridge Philos. Soc. 89(2) (1981) 211–223.
  • [8] R. Chapman, A new proof of some identities of Bressoud, Int. J. Math. Math. Sci. 32(10) (2002) 627–633.
  • [9] N. S. S. Gu, H. Prodinger, On some continued fraction expansions of the Rogers–Ramanujan type, Ramanujan J. 26(3) (2011) 323–367.
  • [10] A. V. Sills, Finite Rogers–Ramanujan type identities, Electron. J. Combin. 10 (2003) Research Paper 13, 122 pp.
  • [11] L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math. Soc. s2–54(1) (1952) 147–167.

Finite Rogers-Ramanujan type continued fractions

Year 2018, Volume: 5 Issue: 3, 137 - 142, 08.10.2018
https://doi.org/10.13069/jacodesmath.451218

Abstract

New finite continued fractions related to Bressoud and Santos polynomials
are established.

References

  • [1] G. E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison–Wesley Publishing Co., Reading, Mass.–London–Amsterdam, 1976.
  • [2] G. E. Andrews, A. Knopfmacher, P. Paule, H. Prodinger, q–Engel series expansions and Slater’s identities, Quaest. Math. 24(3) (2001) 403–416.
  • [3] G. E. Andrews, A. Knopfmacher, P. Paule, An infinite family of Engel expansions of Rogers– Ramanujan type, Adv. Appl. Math. 25(1) (2000) 2–11.
  • [4] G. E. Andrews, J. P. O. Santos, Rogers–Ramanujan type identities for partitions with attached odd parts, Ramanujan J. 1(1) (1997) 91–99.
  • [5] B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer–Verlag, New York, 1991.
  • [6] B. C. Berndt, S. S. Huang, J. Sohn, S. H. Son, Some theorems on the Rogers–Ramanujan continued fraction in Ramanujan’s lost notebook, Trans. Amer. Math. Soc. 352 (2000) 2157–2177.
  • [7] D. M. Bressoud, Some identities for terminating q-series, Math. Proc. Cambridge Philos. Soc. 89(2) (1981) 211–223.
  • [8] R. Chapman, A new proof of some identities of Bressoud, Int. J. Math. Math. Sci. 32(10) (2002) 627–633.
  • [9] N. S. S. Gu, H. Prodinger, On some continued fraction expansions of the Rogers–Ramanujan type, Ramanujan J. 26(3) (2011) 323–367.
  • [10] A. V. Sills, Finite Rogers–Ramanujan type identities, Electron. J. Combin. 10 (2003) Research Paper 13, 122 pp.
  • [11] L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math. Soc. s2–54(1) (1952) 147–167.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Helmut Prodinger 0000-0002-0009-8015

Publication Date October 8, 2018
Published in Issue Year 2018 Volume: 5 Issue: 3

Cite

APA Prodinger, H. (2018). Finite Rogers-Ramanujan type continued fractions. Journal of Algebra Combinatorics Discrete Structures and Applications, 5(3), 137-142. https://doi.org/10.13069/jacodesmath.451218
AMA Prodinger H. Finite Rogers-Ramanujan type continued fractions. Journal of Algebra Combinatorics Discrete Structures and Applications. October 2018;5(3):137-142. doi:10.13069/jacodesmath.451218
Chicago Prodinger, Helmut. “Finite Rogers-Ramanujan Type Continued Fractions”. Journal of Algebra Combinatorics Discrete Structures and Applications 5, no. 3 (October 2018): 137-42. https://doi.org/10.13069/jacodesmath.451218.
EndNote Prodinger H (October 1, 2018) Finite Rogers-Ramanujan type continued fractions. Journal of Algebra Combinatorics Discrete Structures and Applications 5 3 137–142.
IEEE H. Prodinger, “Finite Rogers-Ramanujan type continued fractions”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 5, no. 3, pp. 137–142, 2018, doi: 10.13069/jacodesmath.451218.
ISNAD Prodinger, Helmut. “Finite Rogers-Ramanujan Type Continued Fractions”. Journal of Algebra Combinatorics Discrete Structures and Applications 5/3 (October 2018), 137-142. https://doi.org/10.13069/jacodesmath.451218.
JAMA Prodinger H. Finite Rogers-Ramanujan type continued fractions. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5:137–142.
MLA Prodinger, Helmut. “Finite Rogers-Ramanujan Type Continued Fractions”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 5, no. 3, 2018, pp. 137-42, doi:10.13069/jacodesmath.451218.
Vancouver Prodinger H. Finite Rogers-Ramanujan type continued fractions. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5(3):137-42.