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Generalization of Zernike polynomials for regular portions of circles and ellipses
(Optical Society of America, 2014)
info:eu-repo/semantics/article,
Zernike polynomials are commonly used to represent the
wavefront phase on circular optical apertures, since they form a complete
and orthonormal basis on the unit circle. Here, we present a generalization
of this Zernike ...
A simplification of the stationary phase method: application to the Anger and Weber functions
(Kent State UniversityJohann Radon Institute (RICAM), 2017)
info:eu-repo/semantics/article,
The main difficulty in the practical use of the stationary phase method in asymptotic expansions of
integrals is originated by a change of variables. The coefficients of the asymptotic expansion are the coefficients of
the ...
Convergent expansions of the incomplete gamma functions in terms of elementary functions
(World Scientific Publishing, 2017)
info:eu-repo/semantics/article,
We consider the incomplete gamma function γ(a,z) for Ra>0 and z∈C. We derive several convergent expansions of z−aγ(a,z) in terms of exponentials and rational functions of z that hold uniformly in z with Rz bounded from ...
Zernike-like systems in polygons and polygonal facets
(Optical Society of America, 2015)
info:eu-repo/semantics/article,
Zernike polynomials are commonly used to represent the wavefront phase on circular
optical apertures, since they form a complete and orthonormal basis on the unit disk. In
[Diaz et all, 2014] we introduced a new Zernike ...
On a modifcation of Olver's method: a special case
(Springer US, 2016)
info:eu-repo/semantics/article,
We consider the asymptotic method designed by Olver (Asymptotics and
special functions. Academic Press, New York, 1974) for linear differential equations of
the second order containing a large (asymptotic) parameter : ...
Orthogonal basis with a conicoid first mode for shape specification of optical surfaces
(Optical Society of America, 2016)
info:eu-repo/semantics/article,
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and ...
Convergent and asymptotic expansions of the Pearcey integral
(Elsevier, 2015)
info:eu-repo/semantics/article,
We consider the Pearcey integral P(x; y) for large values of |x|, x, y ∈ C. We can find
in the literature several convergent or asymptotic expansions in terms of elementary and
special functions, with different levels ...
The Pearcey integral in the highly oscillatory region
(Elsevier, 2016)
info:eu-repo/semantics/article,
We consider the Pearcey integral P(x, y) for large values of |y| and bounded values of |x|. The integrand of the Pearcey integral oscillates wildly in this region and the asymptotic saddle point analysis is complicated. ...
Analytic formulas for the evaluation of the Pearcey integral
(American Mathematical Society, 2017)
info:eu-repo/semantics/article,
We can find in the literature several convergent and/or asymptotic
expansions of the Pearcey integral P(x, y) in different regions of the complex
variables x and y, but they do not cover the whole complex x and y ...
Representations of hypergeometric functions for arbitrary parameter values and their use
(2017)
Artículo / Artikulua,
Integral representations of hypergeometric functions proved to be
a very useful tool for studying their properties. The purpose of this paper is
twofold. First, we extend the known representations to arbitrary values of ...