Differential and difference polynomial sequences

Veasna Kim, Vichian Laohakosol and Supawadee Prugsapitak
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 4, Pages 58–65
DOI: 10.7546/nntdm.2019.25.4.58-65
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Authors and affiliations

Veasna Kim
Department of Mathematics and Statistics, Faculty of Science
Prince of Songkla University, Hat Yai 90110, Thailand

Vichian Laohakosol
Department of Mathematics, Faculty of Science
Kasetsart University, Bangkok 10900, Thailand

Supawadee Prugsapitak
Department of Mathematics and Statistics, Faculty of Science
Prince of Songkla University, Hat Yai 90110, Thailand

Abstract

A polynomial sequence is a sequence of n positive integers which represents the
values of an integer polynomial at the first n positive integers. We extend this notion to differential and difference polynomial sequences which are defined analogously by incorporating not only the polynomial values but also the values of its derivatives and/or differences at integer points. Characterizations and their algebraic structures are determined.

Keywords

  • Polynomial sequence
  • Differential polynomial sequence
  • Difference polynomial sequence

2010 Mathematics Subject Classification

  • 11B83
  • 11C08
  • 13G05

References

  1. Cornelius Jr., E. F., & Schultz, P. (2008). Sequences generated by polynomials, Amer. Math. Monthly, 115 (2), 154–158.
  2. Davis, P. J. (1975). Interpolation and Approximation, Dover, New York.
  3. Hartley, B., & Hawkes, T. O. (1974). Rings, Modules and Linear Algebra, Chapman and Hall, London.
  4. Kim, V., Laohakosol, V. & Prugsapitak, S. (2019). Sequences generated by polynomials over integral domains, Walailak J. Sci. Tech., 16 (9), 625–633.
  5. Spitzbart, A. (1960). A generalization of Hermite’s interpolation formula, Amer. Math. Monthly, 67 (1), 42–46.

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Cite this paper

APA

Kim, V., Laohakosol, V. & Prugsapitak, S. (2019). Differential and difference polynomial sequences. Notes on Number Theory and Discrete Mathematics, 25(4), 58-65, doi: 10.7546/nntdm.2019.25.4.58-65.

Chicago

Kim, Veasna, Vichian Laohakosol and Supawadee Prugsapitak. “Differential and Difference Polynomial Sequences.” Notes on Number Theory and Discrete Mathematics 25, no. 4 (2019): 58-65, doi: 10.7546/nntdm.2019.25.4.58-65.

MLA

Kim, Veasna, Vichian Laohakosol and Supawadee Prugsapitak. “Differential and Difference Polynomial Sequences.” Notes on Number Theory and Discrete Mathematics 25.4 (2019): 58-65. Print, doi: 10.7546/nntdm.2019.25.4.58-65.

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