A SERIES EXPANSION FOR THE $b(s)$ BROUNCKER-RAMANUJAN FUNCTION

Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 36

Abstract

Our basic aim is to provide a power series representation for $b(s)$, $0<s<3$, the well-known function satisfying $b(s-1)b(s+1)=s^2$. We will do this by using integer compositions of $n$. In the last section, some properties involving the coefficients of $s^n$ in the power series expansion of $b(s)$ are given, as well an expression for $\frac{4}{\pi}$.

Keywords and Phrases

Brouncker-Ramanujan function, Integer Compositions, Convergent series, Infinite Products, Functional Equations.

A.M.S. subject classification

40B05, 40C15.

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