New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet’s solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is related to the solution of a Mathieu equation of odd characteristic exponent. The number of notches of these analysing filters can be easily designed. Wavelet...

The main purpose of this paper is to present a number of potentially useful integral representations for the familiar Mathieu a-series as well as for its alternating version. These results are derived here from many different considerations and are shown to yield sharp bounding inequalities involving the Mathieu and alternating Mathieu a-series. Relationships of the Mathieu a-series with the Ri...

Closed integral form expressions are derived for the Mathieu-type a-series and for the associated alternating series whose terms contain Fox’s H -function. In the final section, two similar results on Mathieu-type series with the Fox–Wright Psi-function pΨq and the generalized hypergeometric function pFq which can be expressed in terms of Fox’s H -functions are deduced respectively. c © 2006 El...

We propose a homotopy analysis method in combination with Galerkin projections to obtain transition curves of Mathieu-like equations. While constructing homotopy, we think convergence-control parameter as function embedding and call it function. Homotopy provides relation between the parameters Mathieu equation that also includes free arising from generate extra nonlinear algebraic equations us...

Abstract The main objective of this paper is to present a new extension the familiar Mathieu series and alternating S ( r ) $${{\widetilde{S}}}(r)$$ S ~ ( r ) which are denoted by $${\mathbb {S}...

We propose two methods to find analytic periodic approximations intended for differential equations of Hill type. Here, we apply these methods on the simplest case of the Mathieu equation. The former has been inspired in the harmonic balance method and designed to find, making use on a given algebraic function, analytic approximations for the critical values and their corresponding periodic sol...

We apply exact WKB methods to the study of the partition function of pure N = 2 i-deformed gauge theory in four dimensions in the context of the 2d/4d correspondence. We study the partition function at leading order in 2/ 1 (i.e. at large central charge) and in an expansion in 1. We find corrections of the form ∼ exp[− periods 1 ] to this expansion. We attribute these to the exchange of the ord...

Voice production models are used for speech compression thus reducing the encoding data rates and storage space for speech signaling processing. The legacy voice production model consists of a vocal source model and a vocal tract model. This paper presents a simpler voice production model adapted to waveform coding of speech: the Mathieu Waveform Coder (MWC) model. The MWC model yields weighted...

Integral representations for a generalized Mathieu series and its companions are used to undertake analysis leading novel insights Zeta Dirichlet Beta function families. The bounds procured using sharp of family procure approximating utilising integral representation results in particular Hardy-type upper bounds.