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

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 $\frac{4}{\pi}$.