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2012•Journal of Huaiyin Teachers CollegeRequires access

Involving the Multiple Convolution Formula of Fibonacci Number and Lucas Number

Yue Wang

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Abstract

In this paper,it was mainly discussed the relationship of recursiveness on the basis of Fibonacci Number {Fn}and Lucas Number{Ln},researched the generating function of ∑∞n=1Fn2 xn and ∑∞n=1Ln2 xn in relation to Fibonacci Number and Lucas Number.Used the Stirling numbers of the first kind and the Stirling numbers of the second kind,got involved in the multiple convolution formula of Fibonacci Number and Lucas Number,generalized W Chu's related conclusions.

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What this paper is about

In this paper,it was mainly discussed the relationship of recursiveness on the basis of Fibonacci Number {Fn}and Lucas Number{Ln},researched the generating function of ∑∞n=1Fn2 xn and ∑∞n=1Ln2 xn in relation to Fibonacci Number and Lucas Number.Used the Stirling numbers of the first kind and the Stirling numbers of the second kind,got involved in the multiple convolution formula of Fibonacci Number and Lucas Number,generalized W Chu's related conclusions.

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Available abstract

In this paper,it was mainly discussed the relationship of recursiveness on the basis of Fibonacci Number {Fn}and Lucas Number{Ln},researched the generating function of ∑∞n=1Fn2 xn and ∑∞n=1Ln2 xn in relation to Fibonacci Number and Lucas Number.Used the Stirling numbers of the first kind and the Stirling numbers of the second kind,got involved in the multiple convolution formula of Fibonacci Number and Lucas Number,generalized W Chu's related conclusions.

Key concepts: Fibonacci number, Lucas number, Fibonacci polynomials, Lucas sequence, Pisano period, Mathematics, Recurrence relation, Convolution (computer science)

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