On the convergence of second-order recurrence series

Bijan Kumar Patel and Prasanta Kumar Ray
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 4, Pages 120—127
DOI: 10.7546/nntdm.2018.24.4.120-127
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Authors and affiliations

Bijan Kumar Patel
International Institute of Information Technology Bhubaneswar
Bhubaneswar-751003, India

Prasanta Kumar Ray
School of Mathematical Sciences, Sambalpur University
Sambalpur-768019, India

Abstract

In this article, a generalized second-order linear recurrence sequence is considered and the range of the convergence of this sequence with power series is studied. An estimation for the speed of convergence of the second-order linear recurrence series is also given.

Keywords

  • Second-order recurrence relation
  • Power series
  • Range of convergence
  • Speed of convergence

2010 Mathematics Subject Classification

  • 11B39
  • 11B83

References

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  8. Patel, B. K. & Ray, P. K. (2016) The period, rank and order of the sequence of balancing numbers modulo m, Math. Rep. (Bucur.), 18, 395–401.
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  12. Ray, P. K. (2018) On the properties of k-balancing numbers, Ain. Shams Eng. J., 9, 395–402.

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Cite this paper

APA

Patel, B. K., & Ray, P. K. (2018). On the convergence of second-order recurrence series. Notes on Number Theory and Discrete Mathematics, 24(4), 120-127, doi: 10.7546/nntdm.2018.24.4.120-127.

Chicago

Patel, Bijan Kumar and Prasanta Kumar Ray. “On the Convergence of Second-order Recurrence Series.” Notes on Number Theory and Discrete Mathematics 24, no. 4 (2018): 120-127, doi: 10.7546/nntdm.2018.24.4.120-127.

MLA

Patel, Bijan Kumar and Prasanta Kumar Ray. “On the Convergence of Second-order Recurrence Series.” Notes on Number Theory and Discrete Mathematics 24.4 (2018): 120-127. Print, doi: 10.7546/nntdm.2018.24.4.120-127.

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