Infinite Fibonacci Series Arising from Generalized Second Order - Difference Equations
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https://doi.org/10.14419/ijet.v7i4.10.21316
Received date: October 8, 2018
Accepted date: October 8, 2018
Published date: October 2, 2018
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Fibonacci numbers, Second -difference operator and Summation solution, Infinite Multi-series.Use. -
Abstract
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.
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References
- Benjamin AT, Quinn JJ and Su F.E(2000), ”Generalized Fibonacci Identities through Phased Tilings”, The Fibonacci Quarterly, Vol. 38 No. 3, pp. 282-288.
- Xavier GBA, Gerly TG and Kumar SUV(2015), ”Multi-Series Solution of Generalized q-alpha Difference Equation”, International Journal of Applied Engineering Research, Vol. 10 No. 72, pp. 97-101.
- Xavier GBA and Gerly TG(2016), ”Fibonacci Sequence Generated From Two Dimensional -Difference Equation”, International Journal Mathematics And its Applications, Vol. 4. No. 1-B, pp. 67-72.
- Horadam F(1961), ”A generalized Fibonacci sequence”, American Mathematical Monthly, Vol. 68, pp. 455-459.
- Jackson FH(1908), ”On q-functions and a Certain Difference Operator”, Trans. Roy.Soc.Edin, Vol. 46, pp. 64-72.
- Jackson FH, ”On q-definite integrals”, Qust.J. Pure Appl. Math. Vol. 41, pp. 193-203.
- Jerzy Popenda and Blazej Szmanda(1984), On the Oscillation of Solutions of Certain Difference Equations, Demonstratio Mathematica, Vol. 17 No. 1, pp. 153-164.
- Manuel MMS, Xavier GBA and Thandapani E, ”Theory of Generalized Difference Operator and Its Applications”, Far East Journal of Mathematical Sciences, Vol. 20 No. 2, pp. 163-171.
- Miller KS and Ross B(1989), Fractional difference calculus, in ”Univalent functions, fractional calculus and the applications(Koriyama, 1988)”, pp. 139-152.
- Koshy T(2001), ”Fibonacci and Lucas Numbers with Applications”, Wiley, New York.
- Walton JE and Horadam AF(1974), ”Some further identities for the generalized Fibonacci sequence”, 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 and Technology, 7(4.10), 702-705. https://doi.org/10.14419/ijet.v7i4.10.21316
