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
Download full paper: PDF, 150 Kb
Authors and affiliations
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.
- Second-order recurrence relation
- Power series
- Range of convergence
- Speed of convergence
2010 Mathematics Subject Classification
- Behera, A., & Panda, G. K. (1999) On the square roots of triangular numbers, Fibonacci Quart., 37, 98–105.
- Catarino, P., Campos, H., & Vasco, P. (2015) On some identities for balancing and cobalancing numbers, Ann. Math. Inform., 45, 11–24.
- Glaister, P. (1995) Fibonacci power series, Math. Gaz., 79, 521–525.
- Horadam, A. F. (1965) Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3, 161–176.
- Komatsu, T., & Szalay, L. (2014) Balancing with binomial coefficients, Intern. J. Number Theory, 10, 1729–1742.
- Koshy, T. (1999) The Convergence of a Lucas Series, Math. Gaz., 83, 272–274.
- Koshy, T. (2012) Convergence of Pell and Pell–Lucas Series, Math. Spectr., 45, 10–13.
- 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.
- Ray, P. K. (2014) Some congruences for balancing and Lucas-balancing numbers and their applications, Integers, 14, #A8.
- Ray, P. K. (2015) Balancing and Lucas-balancing sums by matrix methods, Math. Rep. (Bucur.), 17, 225–233.
- Ray, P. K., & Patel, B. K. (2016) Uniform distribution of the sequence of balancing numbers modulo m, Unif. Distrib. Theory, 11, 15–21.
- Ray, P. K. (2018) On the properties of k-balancing numbers, Ain. Shams Eng. J., 9, 395–402.
Cite this paperAPA
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.