Document Type

Article

Publication Date

2010

Abstract

Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined by r1(x) =: ∑∞ n=0 anx n , r2(x) =: ∑∞ n=0 bnx n and r3(x) =: ∑∞ n=0 cnx n (here each ri(x) is a certain rational function in x), then a 3 n + b 3 n − c 3 n = (−1)n , ∀ n ≥ 0. Motivated by this amazing identity, we state and prove a more general identity involving eleven sequences, the new identity being ”more general” in the sense that equality holds not just for the power 3 (as in Ramanujan’s identity), but for each power j, 1 ≤ j ≤ 5.

Publication Title

The Fibonacci Quarterly

Publisher

Canadian Mathematical Society and Dalhousie University

Volume

48

Issue

1

First Page

34

Last Page

38

Comments

Preprint version is available here.

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