arXiv subjects
Publications and source records attributed to Soumon Roy.
In this note, we present an integral representation of the $k$-generalized Fibonacci sequence and provide a proof using contour integration. This representation enables the derivation of several known identities and a Binet-type formula related to the $k$-generalized Fibonacci sequence.
This paper aims to study the periodicity of a transcendental entire function of hyper-order less than one. For a transcendental entire function of hyper order less than one and a non-zero complex constant $c$, $\mathfrak{f} (z) \equiv \mathfrak{f} (z + c)$ if they share a certain set with weight two.
Let $\mathfrak{f}$ be a transcendental entire function with hyper-order less than one. The aim of this note is to study the value distribution of the differential-difference monomials $α\mathfrak{f}(z)^{q_0}(\mathfrak{f}(z+c))^{q_1}$, where $c$ is a non-zero complex number and $q_0\geq2,$ $q_1\geq 1$ are non-negative integers, and $ α(z)$ $(\not\equiv 0,\infty)$ be a small function of $\mathfrak{f}$.
In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two.