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By virtue of Baileys well-known bilateral 6psi_6 summation formula and Watsons transformation formula,we extend the four-variable generalization of Ramanujans reciprocity theorem due to Andrews to a five-variable one. Some relevant new q-series identities including a new proof of Ramanujans reciprocity theorem and of Watsons quintuple product identity only based on Jacksons transformation are presented.
Let $n$ be a positive integer. In 1915, Theisinger proved that if $nge 2$, then the $n$-th harmonic sum $sum_{k=1}^nfrac{1}{k}$ is not an integer. Let $a$ and $b$ be positive integers. In 1923, Nagell extended Theisingers theorem by showing that the
Recently, Corvaja and Zannier obtained an extension of the Subspace Theorem with arbitrary homogeneous polynomials of arbitrary degreee instead of linear forms. Their result states that the set of solutions in P^n(K) (K number field) of the inequalit
Let $G$ be a connected reductive group over a $p$-adic local field $F$. We propose and study the notions of $G$-$varphi$-modules and $G$-$(varphi, abla)$-modules over the Robba ring, which are exact faithful $F$-linear tensor functors from the catego
In 1730 James Stirling, building on the work of Abraham de Moivre, published what is known as Stirlings approximation of $n!$. He gave a good formula which is asymptotic to $n!$. Since then hundreds of papers have given alternative proofs of his resu
We define a new parameter $A_{k,n}$ involving Ramanujans theta-functions for any positive real numbers $k$ and $n$ which is analogous to the parameter $A_{k,n}$ defined by Nipen Saikia cite{NS1}. We establish some modular relation involving $A_{k,n}$