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.
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
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.
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.