A simplified overview of certain relations among infinite series that arose in the context of fractional calculus

AbstractAn interesting infinite series relation was proven recently by applying a certain known generalization of the Riemann-Liouville and Erdélyi-Kober operators of fractional calculus. In our attempt to give a much simpler proof of this result, without using the generalized fractional calculus operator, we are led here to another class of infinite series relations. Some relevant connections with a number of known results are also indicated

Some multiple integral transformations involving the H-function of several variables

AbstractThe object of the present paper is to give two general multiple integral transformations of the H-function of several complex variables, which was defined and studied elsewhere by the authors (cf., e.g., [10], [11] and [12]). It is shown how the main formulas (1,8) and (1,14) below, involving Fox's H-function ([4], p, 408) and the Laguerre polynomials, respectively, are related to each other and, of course, to a number of results given recently in the literature (see [1] and [5] through [9]). Several possible applications of the operational techniques provided by these results (and their various special cases) when viewed as multidimensional integral transformations are also indicated briefly

Query Expansion Strategy based on Pseudo Relevance Feedback and Term Weight Scheme for Monolingual Retrieval

Query Expansion using Pseudo Relevance Feedback is a useful and a popular technique for reformulating the query. In our proposed query expansion method, we assume that relevant information can be found within a document near the central idea. The document is normally divided into sections, paragraphs and lines. The proposed method tries to extract keywords that are closer to the central theme of the document. The expansion terms are obtained by equi-frequency partition of the documents obtained from pseudo relevance feedback and by using tf-idf scores. The idf factor is calculated for number of partitions in documents. The group of words for query expansion is selected using the following approaches: the highest score, average score and a group of words that has maximum number of keywords. As each query behaved differently for different methods, the effect of these methods in selecting the words for query expansion is investigated. From this initial study, we extend the experiment to develop a rule-based statistical model that automatically selects the best group of words incorporating the tf-idf scoring and the 3 approaches explained here, in the future. The experiments were performed on FIRE 2011 Adhoc Hindi and English test collections on 50 queries each, using Terrier as retrieval engine

Construction of a new family of Fubini-type polynomials and its applications

This paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introduce new families of special polynomials. Motivation of this paper is to construct a new class of generalized Fubini-type polynomials of the parametric kind via operational view point. The generating functions, differential equations, and other properties for these polynomials are established within the context of the monomiality principle. Using the generating functions, various interesting identities and relations related to the generalized Fubini-type polynomials are derived. Further, we obtain certain partial derivative formulas including the generalized Fubini-type polynomials. In addition, certain members belonging to the aforementioned general class of polynomials are considered. The numerical results to calculate the zeros and approximate solutions of these polynomials are given and their graphical representation are shown. © 2021, The Author(s)

Separation Axioms in Intuitionistic Fuzzy Topological Spaces

In this paper we have studied separation axioms , in an intuitionistic fuzzy topological space introduced by Coker. We also show the existence of functors and and observe that is left adjoint to