Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences

References (13)

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