The translated logarithmic Lambert function is defined and basic analytic properties of the are obtained including derivative, integral, Taylor series expansion, real branches asymptotic approximation function. Moreover, probability distribution three-parameter entropy derived which expressed in terms

In this paper we study the properties of coefficients appearing in the series expansions for zeros of generalized Rogers-Ramanujan series. Our primary purpose is to address several conjectures made by M. E. H Ismail and C. Zhang. We prove that the coefficients in the series expansion of each zero approach rational multiples of π and π as q → 1−. We also show that certain polynomials arising in ...

First year students learn that the Taylor expansion Z carries functions into power series, and that it has some nice algebraic properties (e.g., Z (fg) = Z (f)Z (g)). It is less well known that the same game can be played within arbitrary groups: there is a natural way to say “a Taylor expansion Z for elements of an arbitrary group G”, and a natural way to carry the algebraic properties of the ...

We explore a function theory connected with the principal series representation of SL(2, R) in contrast to standard complex analysis connected with the discrete series. We construct counterparts for the Cauchy integral formula, the Hardy space, the Cauchy-Riemann equation and the Taylor expansion. ∗Supported by grant 3GP03196 of the FWO-Vlaanderen (Fund of Scientific ResearchFlanders), Scientif...

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We explore a function theory connected with the principal series representation of SL(2, R) in contrast to standard complex analysis connected with the discrete series. We construct counterparts for the Cauchy integral formula, the Hardy space, the Cauchy-Riemann equation and the Taylor expansion. ∗Supported by grant 3GP03196 of the FWO-Vlaanderen (Fund of Scientific ResearchFlanders), Scientif...