On the singularities of Gegenbauer (ultraspherical) expansions

On Rapid Computation of Expansions in Ultraspherical Polynomials

We present an O(N log2 N) algorithm for the computation of the first N coefficients in the expansion of an analytic function in ultraspherical polynomials. We first represent expansion coefficients as an infinite linear combination of derivatives and then as an integral transform with a hypergeometric kernel along the boundary of a Bernstein ellipse. Following a transformation of the kernel, we...

Calderón-zygmund Operators Associated to Ultraspherical Expansions

Reconstruction of sparse Legendre and Gegenbauer expansions

Recently the reconstruction of sparse trigonometric polynomials has attained much attention. There exist recovery methods based on random sampling related to compressed sensing (see e.g. [17, 10, 5, 4] and the references therein) and methods based on deterministic sampling related to Prony–like methods (see e.g. [15] and the references therein). Both methods are already generalized to other pol...

Computing with Expansions in Gegenbauer Polynomials

In this work, we develop fast algorithms for computations involving finite expansions in Gegenbauer polynomials. We describe a method to convert a linear combination of Gegenbauer polynomials up to degree n into a representation in a different family of Gegenbauer polynomials with generally O(n log(1/ε)) arithmetic operations where ε is a prescribed accuracy. Special cases where source or targe...

survey on the rule of the due & hindering relying on the sheikh ansaris ideas

قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...