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Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences

Yıl 2019, Cilt: 11 Sayı: 1, 53 - 57, 30.06.2019

Öz

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.

Kaynakça

  • 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.
Yıl 2019, Cilt: 11 Sayı: 1, 53 - 57, 30.06.2019

Öz

Kaynakça

  • 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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Gül Özkan Kızılırmak 0000-0003-3263-8685

Dursun Taşcı

Yayımlanma Tarihi 30 Haziran 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 11 Sayı: 1

Kaynak Göster

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. Haziran 2019;11(1):53-57.
Chicago Özkan Kızılırmak, Gül, ve Dursun Taşcı. “Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences”. Turkish Journal of Mathematics and Computer Science 11, sy. 1 (Haziran 2019): 53-57.
EndNote Özkan Kızılırmak G, Taşcı D (01 Haziran 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 ve D. Taşcı, “Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences”, TJMCS, c. 11, sy. 1, ss. 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 (Haziran 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 ve Dursun Taşcı. “Lambert Series in the Summation of Reciprocals in Gaussian Fibonacci Sequences”. Turkish Journal of Mathematics and Computer Science, c. 11, sy. 1, 2019, ss. 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.