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In his paper [2], Chongdar obtained an extension (Theorem 3) of the result on bilateral generating functions involving modified Laguerre polynomial stated in Theorem 1 of Ghosh [3]. In this article, the present authors have made an attempt to present a further generalization of the extension obtained by Chongdar [2] by means of the theory of one parameter group of continuous transformations as well as using the concepts of partial quasibilateral generating function [4] involving some special functions.

Abstract The objective of this work is to develop graphene oxide (GO) incorporated butyl rubber (IIR) nanocomposites by three different methods: direct addition approach (DAAM), single step method (SSM) and two step method (TSM). Chlorobutyl rubber was used as a compatibilizer in SSM and TSM. Mechanical properties of developed nanocomposites was increased and gas permeability co-efficient was decreased up on addition of GO content in IIR matrix. Maximum technical properties was achieved for the nanocomposite with 1.6 wt.% of GO in all methods was achieved due to better interfacial bonding with IIR matrix. When GO content increases above 1.6 wt.% in IIR matrix leads to agglomeration which resulted in deterioration of mechanical properties. HR-TEM studies revealed that nanocomposites prepared by TSM shows exfoliated structure of GO in IIR matrix due to homogenous distribution when compared to the nanocomposites prepared with DAAM and SSM.