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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## Details

### 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

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

## Related papers

## Cite this paper

APAKim, 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.

ChicagoKim, 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.

MLAKim, 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.