Infinite Fibonacci Series Arising from Generalized Second Order - Difference Equations

  • Authors

    • G. Britto Antony Xavier
    • B. Mohan
    • T. G. Gerly
    • R. Suganya
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.21316
  • Fibonacci numbers, Second -difference operator and Summation solution, Infinite Multi-series.Use.

  • In this paper, we extend finite Second order -Fibonacci formula to infinite Second order -Fibonacci formula and also obtain the sum of infinite Second order -Fibonacci multi-series formula. Suitable examples are inserted to illustrate our findings.

     

  • References

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      [2] Xavier GBA, Gerly TG and Kumar SUV(2015), â€Multi-Series Solution of Generalized q-alpha Difference Equationâ€, International Journal of Applied Engineering Research, Vol. 10 No. 72, pp. 97-101.

      [3] Xavier GBA and Gerly TG(2016), â€Fibonacci Sequence Generated From Two Dimensional -Difference Equationâ€, International Journal Mathematics And its Applications, Vol. 4. No. 1-B, pp. 67-72.

      [4] Horadam F(1961), â€A generalized Fibonacci sequenceâ€, American Mathematical Monthly, Vol. 68, pp. 455-459.

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      [7] Jerzy Popenda and Blazej Szmanda(1984), On the Oscillation of Solutions of Certain Difference Equations, Demonstratio Mathematica, Vol. 17 No. 1, pp. 153-164.

      [8] Manuel MMS, Xavier GBA and Thandapani E, â€Theory of Generalized Difference Operator and Its Applicationsâ€, Far East Journal of Mathematical Sciences, Vol. 20 No. 2, pp. 163-171.

      [9] Miller KS and Ross B(1989), Fractional difference calculus, in â€Univalent functions, fractional calculus and the applications(Koriyama, 1988)â€, pp. 139-152.

      [10] Koshy T(2001), â€Fibonacci and Lucas Numbers with Applicationsâ€, Wiley, New York.

      [11] Walton JE and Horadam AF(1974), â€Some further identities for the generalized Fibonacci sequenceâ€, Fibonacci Quart. Vol. 12, pp. 272-280.

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  • How to Cite

    Britto Antony Xavier, G., Mohan, B., G. Gerly, T., & Suganya, R. (2018). Infinite Fibonacci Series Arising from Generalized Second Order - Difference Equations. International Journal of Engineering & Technology, 7(4.10), 702-705. https://doi.org/10.14419/ijet.v7i4.10.21316