Degenerate exponential integral function and its properties

Abstract

PurposeIn this paper, the author introduces a degenerate exponential integral function and further studies some of its analytical properties. The new function is a generalization of the classical exponential integral function and the properties established are analogous to those satisfied by the classical function.Design/methodology/approachThe methods adopted in establishing the results are theoretical in nature.FindingsA degenerate exponential integral function which is a generalization of the classical exponential integral function has been introduced and its properties investigated. Upon taking some limits, the established results reduce to results involving the classical exponential integral function.Originality/valueThe results obtained in this paper are new and have the potential of inspiring further research on the subject.

Some Properties of the Degenerate Hyperbolic Functions

“…for λ ∈ (0, ∞) and t ∈ R. Figures 1,2,3,4,5 and 6 below, are the plots of the degenerate hyperbolic cosine, sine, tangent, secant, cosecant and cotangent functions respectively. The introduction of the degenerate hyperbolic functions was motivated by the degenerate exponential function, which is well known in the literature (see [2], [3], [4], [5], [6], [7]), and the recent interest of many reseachers in establishing degenerate versions of some special functions(see [8], [9]). In [10], the hyperbolic secant function has been applied to handle noise in data processing.…”

Inequalities for Means Regarding the Trigamma Function

“…For similar results involving other special functions, one may refer to the works [14,15,16,17,18,19,20].…”