Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker–Kotel'nikov–Shannon (WKS) sampling restoration sum for Bernstein function classes B q π,d , q > 1, d ∈ N, when the decay rate of the sampled functions is unknown. The case of regular sampling is discussed. Extremal properties of related series of sinc functions are investigated.

An attempt is made here to study the Mittag–Leffler function with two variables. Its various properties including integral and operational relationships other known functions of one variable, pure differential recurrence relations, Euler transform, Laplace Mellin Whittaker Mellin–Barnes representation, its relationship Wright hypergeometric are investigated established. Also, variables associat...

We prove a motivic analogue of the Weyl character formula, computing Euler characteristic line bundle on generalized ag manifold G/B multiplied either by Chern class Schubert cell, or Segre it. The result, given in terms Demazure–Lusztig (D–L) operators, identifies an above to formula Brubaker, Bump and Licata for Iwahori–Whittaker functions principal series representation p-adic Langlands dual...

We define Whittaker modules for the twisted Heisenberg-Virasoro algebra and obtain analogues to several results from the classical setting, including a classification of simple Whittaker modules by central characters.

In this paper, we shall establish a hierarchy of functional equations (as G-function hierarchy) by unifying zeta-functions that satisfy the Hecke equation and those corresponding to Maass forms in framework ramified with (essentially) two gamma factors through Fourier–Whittaker expansion. This unifies theory Epstein associated sense gives method construction forms. long term, is remote conseque...

Many topographic characteristics of the landscape (e.g. relief, slope, aspect, gradient, slope curvature, slope length and contour curvature) play important roles in the distribution of vegetation and biodiversity (e.g. Merriam, 1890, 1894; Whittaker & Niering, 1965, 1968; Vuilleumier, 1970; Brown, 1971, 1978; Hastings et al., 1972; Simpson, 1975; Hanawalt & Whittaker, 1976; Whittaker, 1977; Be...

Special functions such as hypergeometric, zeta, Bessel, Whittaker, Struve, Airy, Weber-Hermite and Mittag-Leffler are obtained a solution to complex differential equations in engineering, science technology. In this work, generalized Euler-type integrals involving four parameters function proposed. Some special cases of type that corresponding well-known results the literature also inferred.

First derivatives with respect to the parameters of Whittaker function $\mathrm{W}_{\kappa ,\mu }\left( x\right) $ are calculated. Using confluent hypergeometric function, these derivarives can be expressed as infinite sums quotients digamma and gamma functions. Also, it is possible obtain parameter in terms integrals integrands containing elementary functions (products algebraic, exponential l...

In this paper a numerical algorithm is proposed for the computation of the Fourier Transform. The quadrature rule developed is based on the Whittaker Cardinal Function expansion of the integrand and a certain Conformai Map. The error of the method is analyzed and numerical results are reported which confirm the accuracy of the quadrature rule.