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Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences

Year 2019, Volume: 11 Issue: 1, 53 - 57, 30.06.2019

Gül Özkan Kızılırmak Dursun Taşcı

Abstract

In this paper, we consider infinite sums derived from the reciprocals of the Gaussian Fibonacci numbers. New expressions of these sums are obtained in terms of Lambert series.

Keywords

Gaussian Fibonacci number Reciprocal sum Lambert series

References

  • Berzseny, G., Gaussian Fibonacci numbers, Fibonacci Quarterly, 15(1977), 233--236.
  • Bilgici, G., Two generalizations of Lucas sequence, Applied Mathematics and Computation, 245(2014), 526--538.
  • Bolat, C., Köse H., On the properties of k-Fibonacci numbers, Int. J. Contemp. Math. Sciences, 5(2010), 1097--1105.
  • Edson, M., Yayenie, O., A new generalization of Fibonacci sequence and extended binet's formula}, Integers, 9(2009), 639--654.
  • Elsner, C., Shimomura, S., ShiokawaI. I., Algebraic relations for reciprocal sums of Fibonacci numbers, Acta Arith., 130(2007), 37--60.
  • Elsner, C., Shimomura, S., ShiokawaI. I., Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers, Ramanujan J., 17(2008), 429--446.
  • Falcon, S., Plaza, A., On the Fibonacci k-numbers, Chaos Soliton Fract., 32(2007), 1615--1624.
  • Falcon, S., On the k-Lucas numbers, Int. J. Contemp. Math. Sciences, 6(2011),1039--1050.
  • Horadam, A. F., Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70(1963), 289--291.
  • Horadam, A. F., Elliptic functions and Lambert series in the summation of reciprocals in certain recurrence-generated sequences, Fibonacci Quarterly, 26(1988), 98--114.
  • Jordan, J.H., Gaussian Fibonacci and Lucas numbers, Fibonacci Quarterly, 3(1965), 315--318.
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, New York, 2001.
  • Ohtsuka, H., Nakamura, S., On the sum of reciprocal Fibonacci numbers, Fibonacci Quart., 46/47(2008/2009), 153--159.

Year 2019, Volume: 11 Issue: 1, 53 - 57, 30.06.2019

Gül Özkan Kızılırmak Dursun Taşcı

Abstract

References

  • Berzseny, G., Gaussian Fibonacci numbers, Fibonacci Quarterly, 15(1977), 233--236.
  • Bilgici, G., Two generalizations of Lucas sequence, Applied Mathematics and Computation, 245(2014), 526--538.
  • Bolat, C., Köse H., On the properties of k-Fibonacci numbers, Int. J. Contemp. Math. Sciences, 5(2010), 1097--1105.
  • Edson, M., Yayenie, O., A new generalization of Fibonacci sequence and extended binet's formula}, Integers, 9(2009), 639--654.
  • Elsner, C., Shimomura, S., ShiokawaI. I., Algebraic relations for reciprocal sums of Fibonacci numbers, Acta Arith., 130(2007), 37--60.
  • Elsner, C., Shimomura, S., ShiokawaI. I., Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers, Ramanujan J., 17(2008), 429--446.
  • Falcon, S., Plaza, A., On the Fibonacci k-numbers, Chaos Soliton Fract., 32(2007), 1615--1624.
  • Falcon, S., On the k-Lucas numbers, Int. J. Contemp. Math. Sciences, 6(2011),1039--1050.
  • Horadam, A. F., Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70(1963), 289--291.
  • Horadam, A. F., Elliptic functions and Lambert series in the summation of reciprocals in certain recurrence-generated sequences, Fibonacci Quarterly, 26(1988), 98--114.
  • Jordan, J.H., Gaussian Fibonacci and Lucas numbers, Fibonacci Quarterly, 3(1965), 315--318.
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, New York, 2001.
  • Ohtsuka, H., Nakamura, S., On the sum of reciprocal Fibonacci numbers, Fibonacci Quart., 46/47(2008/2009), 153--159.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Gül Özkan Kızılırmak 0000-0003-3263-8685

Dursun Taşcı

Publication Date June 30, 2019
Published in Issue Year 2019 Volume: 11 Issue: 1

Cite

APA Özkan Kızılırmak, G., & Taşcı, D. (2019). Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences. Turkish Journal of Mathematics and Computer Science, 11(1), 53-57.
AMA Özkan Kızılırmak G, Taşcı D. Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences. TJMCS. June 2019;11(1):53-57.
Chicago Özkan Kızılırmak, Gül, and Dursun Taşcı. “Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences”. Turkish Journal of Mathematics and Computer Science 11, no. 1 (June 2019): 53-57.
EndNote Özkan Kızılırmak G, Taşcı D (June 1, 2019) Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences. Turkish Journal of Mathematics and Computer Science 11 1 53–57.
IEEE G. Özkan Kızılırmak and D. Taşcı, “Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences”, TJMCS, vol. 11, no. 1, pp. 53–57, 2019.
ISNAD Özkan Kızılırmak, Gül - Taşcı, Dursun. “Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences”. Turkish Journal of Mathematics and Computer Science 11/1 (June 2019), 53-57.
JAMA Özkan Kızılırmak G, Taşcı D. Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences. TJMCS. 2019;11:53–57.
MLA Özkan Kızılırmak, Gül and Dursun Taşcı. “Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences”. Turkish Journal of Mathematics and Computer Science, vol. 11, no. 1, 2019, pp. 53-57.
Vancouver Özkan Kızılırmak G, Taşcı D. Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences. TJMCS. 2019;11(1):53-7.