Rangarajan, R. and Honnegowda, C. K. (2018) Binet forms involving golden ratio and two variables: Convolution identities. Journal of Informatics and Mathematical Sciences, 10 (1-2). ISSN 0975-5748
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The irrational number Φ=1+5√2 or ϕ=−1+5√2 is well known as golden ratio.The binet forms Ln=Φn+(−ϕ)n and Fn=Φn−(−ϕ)np5√ define the well known Lucas and Fibonacci numbers. In the present paper, we generalize the binet forms Φn(x,y)=1y⋅5√[(x+yΦ)n−(x−yϕ)n] and πn(x,y)=[(x+yΦ)n+(x−yϕ)n]. As a result we obtain a pair of two variable polynomial which are new combinatorial entities. Many convolution identities of Ln and Fn are getting added to the recent literature. A generalized convolution identities will be a worthy enrichment of such combinatorial identities to the current literature.
| Item Type: | Article |
|---|---|
| Subjects: | E Mathematical Science > Mathematics |
| Divisions: | Department of > Mathematics |
| Depositing User: | Manjula P Library Assistant |
| Date Deposited: | 14 Aug 2019 07:51 |
| Last Modified: | 02 Nov 2019 10:36 |
| URI: | http://eprints.uni-mysore.ac.in/id/eprint/6358 |
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