Let $\{F_{n}\}_{n\geq0}$ be the Fibonacci sequence. The aim of this paper is to give explicit formulae for infinite products $$\begin{equation*} \prod_{n=1}^{\infty}\left( 1+\frac{1}{F_{n}}\right) ,\quad\prod_{n=3}^{\infty}\left( 1-\frac{1}{F_{n}}\right) \end{equation*}$$ in terms values Jacobi theta functions. From we deduce algebraic independence over $\mathbf{Q}$ above numbers by applying Be...

Sum rules for products of two, three and four QCD currents are derived using chiral symmetry at infinite momentum in the large-N limit. These exact relations among meson decay constants, axialvector couplings and masses determine the asymptotic behavior of an infinite number of QCD correlators. The familiar spectral function sum rules for products of two QCD currents are among the relations der...

We will tackle a conjecture of S. Seo and A. J. Yee, which says that the series expansion $1/(q,-q^3;q^4)_\infty$ has nonnegative coefficients. Our approach relies on an approximation generally nonmodular infinite product $1/(q^a;q^M)_\infty$, where $M$ is positive integer $a$ any $1,2,\ldots,M$.