UNLABELLED This paper deals with the study of a generalized function of Mittag-Leffler type. Various properties including usual differentiation and integration, Euler(Beta) transforms, Laplace transforms, Whittaker transforms, generalized hypergeometric series form with their several special cases are obtained and relationship with Wright hypergeometric function and Laguerre polynomials is also...

In this paper, we study Whittaker modules for a Lie algebras of Block type. We define Whittaker modules and under some conditions, obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules over this algebra and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra.

In this paper, Whittaker modules for the W -algebra W (2, 2) are studied. We obtain analogues to several results from the classical setting and the case of the Virasoro algebra, including a classification of simple Whittaker modules by central characters and composition series for general Whittaker modules.

Let n be an integer and let F be a nonarchimedean local field whose characteristic is not a prime dividing n. Let μk be the group of k-th roots of unity in the algebraic closure of F ; we assume that μ2n ⊂ F . Let G be a split, simply-connected semisimple algebraic group over F . We assume that G is actually defined over the ring o of integers in F in such a way that K = G(o) is a special maxim...

We study the generalized Whittaker models for G = GSp(2,R) associated with indefinite binary quadratic forms when they arise from two standard representations of G: (i) a generalized principal series representation induced from the non-Siegel maximal parabolic subgroup and (ii) a (limit of) large discrete series representation. We prove the uniqueness of such models with moderate growth propert...

We show that closed, radiation-filled Friedmann-Robertson-Walker quantum universes of arbitrary factor ordering obey the Whittaker equation. We also present the formal Witten factorization as well as the double Darboux strictly isospectral scheme for the Whittaker equation. If in the " time-time " component of Einstein's equations for Friedmann-Robertson-Walker (FRW) universes ˙ a 2 + k = 8πG 3...

<p style='text-indent:20px;'>In this article, we have investigated certain definite integrals and various integral transforms of the generalized multi-index Bessel function, such as Euler transform, Laplace Whittaker K-transform Fourier transforms. Also found applications problem on fractional kinetic equation pertaining to function using Sumudu transform technique. Mittage-Leffler is use...

As generalizations of Uq(sl2), a class of algebras Uq(f(K)) were introduced and studied in [7]. For some special parameters f(K) = a(Km − K−m), a 6= 0, m ∈ N, Uq(f(K)) are Hopf algebras and hence quantum groups in the sense of Drinfeld ([3]). In this paper, we realize these algebras as Hyperbolic algebras ([12]). As an application of this realization, we obtain a natural construction of irreduc...