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Temperature-dependent surface diffusion near a grain boundary

JOURNAL OF ENGINEERING MATHEMATICS 2010年第1-3期66卷 87-102页

作者： Broadbridge, P. Goard, J. M. La Trobe Univ Sch Engn & Math Sci Bundoora Vic 3086 Australia Univ Wollongong Sch Math & Appl Stat Wollongong NSW 2522 Australia

Metal surface evolution is described by a nonlinear fourth-order partial differential equation for curvature-driven flow. The standard boundary conditions for grain-boundary grooving, at a grain-grain-fluid triple intersection, involve a prescribed slope at the groove axis. The well-known similarity reduction is no longer valid when the dihedral angle and surface diffusivity depend on time due to variation of the surface temperature. We adapt a nonlinear fourth-order model that can be discerned from symmetry analysis to be integrable, equivalent to the fourth-order linear diffusion equation. The connection between classical symmetries and separation of variables allows us to develop the correction to the self-similar approximation as a power series in a time-like variable.

关键词： Free boundary generalized hypergeometric functions Integrable model Surface diffusion Symmetry reductions

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Incomplete exponential and hypergeometric functions with applications to the non central x²-distribution

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2005年第3期34卷 525-535页

作者： Chaudhry, MA Qadir, A King Fahd Univ Petr & Minerals Dept Math Sci Dhahran 31261 Saudi Arabia Quaid I Azam Univ Dept Math Islamabad Pakistan

Corresponding to the incomplete gamma functions, found useful in many problems, we propose incomplete exponential functions. Like the generalized incomplete gamma functions, the proposed functions have an additional parameter. It is shown that these functions can be related to Bessel functions. This leads us naturally to an incomplete extension of the hypergeometric function. The usefulness of these functions in some closed form representation of the non central chi(2)-distributions is demonstrated.

关键词： Bessel functions cumulative distribution function generalized hypergeometric functions incomplete gamma functions non central x(2)-distributions

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Pearson equations for discrete orthogonal polynomials: III-Christoffel and Geronimus transformations

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2022年第4期116卷 1-23页

作者： Manas, Manuel Univ Complutense Madrid Dept Fis Teor Plaza Ciencias 1 Madrid 28040 Spain Inst Ciencias Matemat ICMAT Campus Cantoblanco UAM Madrid 28049 Spain

Contiguous hypergeometric relations for semiclassical discrete orthogonal polynomials are described as Christoffel and Geronimus transformations. Using the Christoffel-Geronimus-Uvarov formulas quasi-determinantal exp... 详细信息

关键词： Discrete orthogonal polynomials Pearson equations Cholesky factorization generalized hypergeometric functions Contigous relations Christoffel transformations Geronimus transformations Geronimus-Uvarov transformations

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Classes of series identities and associated hypergeometric reduction formulas

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APPLIED MATHEMATICS AND COMPUTATION 2009年第1期215卷 118-124页

作者： Srivastava, Rekha Univ Victoria Dept Math & Stat Victoria BC V8W 3R4 Canada

The main object of the present paper is to investigate some classes of series identities and their applications and consequences leading naturally to several (known or new) hypergeometric reduction formulas. We also indicate how some of these series identities and reduction formulas would yield several series identities which emerged recently in the context of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order). (C) 2009 Elsevier Inc. All rights reserved.

关键词： Series identities Operators of fractional calculus Gamma function Fractional differintegral formulas generalized hypergeometric functions Fox-Wright functions Gauss hypergeometric function F and H functions hypergeometric transformation formulas hypergeometric reduction formulas Legendre's duplication formula Fractional differintegral operator Cauchy-Goursat integral formula

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The Gauss hypergeometric covariance kernel for modeling second-order stationary random fields in Euclidean spaces: its compact support, properties and spectral representation

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2022年第9期36卷 2819-2834页

作者： Emery, Xavier Alegria, Alfredo Univ Chile Dept Min Engn Ave Beauchef 850 Santiago Chile Univ Chile Adv Min Technol Ctr Ave Beauchef 850 Santiago Chile Univ Tecn Federico Santa Maria Dept Matemat Ave Espana 1680 Valparaiso Chile

This paper presents a parametric family of compactly-supported positive semidefinite kernels aimed to model the covariance structure of second-order stationary isotropic random fields defined in the d-dimensional Euclidean space. Both the covariance and its spectral density have an analytic expression involving the hypergeometric functions F-2(1) and F-1(2), respectively, and four real-valued parameters related to the correlation range, smoothness and shape of the covariance. The presented hypergeometric kernel family contains, as special cases, the spherical, cubic, penta, Askey, generalized Wendland and truncated power covariances and, as asymptotic cases, the Matern, Laguerre, Tricomi, incomplete gamma and Gaussian covariances, among others. The parameter space of the univariate hypergeometric kernel is identified and its functional properties-continuity, smoothness, transitive upscaling (montee) and downscaling (descente)-are examined. Several sets of sufficient conditions are also derived to obtain valid stationary bivariate and multivariate covariance kernels, characterized by four matrix-valued parameters. Such kernels turn out to be versatile, insofar as the direct and cross-covariances do not necessarily have the same shapes, correlation ranges or behaviors at short scale, thus associated with vector random fields whose components are cross-correlated but have different spatial structures.

关键词： Positive semidefinite kernels Spectral density Direct and cross-covariances generalized hypergeometric functions Conditionally negative semidefinite matrices Multiply monotone functions

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Neoteric formulas of the monic orthogonal Chebyshev polynomials of the sixth-kind involving moments and linearization formulas

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ADVANCES IN DIFFERENCE EQUATIONS 2021年第1期2021卷 1-19页

作者： Abd-Elhameed, Waleed M. Youssri, H. Youssri Cairo Univ Dept Math Fac Sci Giza 12613 Egypt

The principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The connection coefficients are expressed in terms of terminating hypergeometric functions of certain arguments;however, they can be reduced in some cases. New moment formulas of the sixth-kind Chebyshev polynomials are also established, and in virtue of such formulas, linearization formulas of these polynomials are developed.

关键词： Chebyshev polynomials Connection coefficients Zeilberger's and Petkovsek's algorithms generalized hypergeometric functions Moment formulas Linearization problems 33-XX 33Cxx 42C05

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Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2015年第1期427卷 377-398页

作者： Baeder, Michael A. Cohl, Howard S. Volkmer, Hans Harvey Mudd Coll Dept Math Claremont CA 91711 USA NIST Appl & Computat Math Div Gaithersburg MD 20899 USA Univ Wisconsin Dept Math Sci Milwaukee WI 53201 USA

We use connection relations and series rearrangement to generalize generating functions for several higher continuous orthogonal polynomials in the Askey scheme, namely the Wilson, continuous dual Hahn, continuous Hahn, and Meixner-Pollaczek polynomials. We also determine corresponding definite integrals using the orthogonality relations for these polynomials. Published by Elsevier Inc.

关键词： Orthogonal polynomials Generating functions Connection coefficients generalized hypergeometric functions Eigenfunction expansions Definite integrals

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Meijer's G-Function and Euler's Differential Equation Revisited

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COMPUTATIONAL METHODS AND FUNCTION THEORY 2024年 1-23页

作者： Gesztesy, Fritz Hunziker, Markus Baylor Univ Dept Math Sid Richardson Bldg 1410 S 4th St Waco TX 76706 USA

We consider the generalized eigenvalue problem for the classical Euler differential equation and demonstrate its intimate connection with Meijer's G-functions. In the course of deriving the solution of the generalized Euler eigenvalue equation we review some of the basics of generalized hypergeometric functions and Meijer's G-functions and some of its special cases where the underlying Mellin-type integrand exhibits higher-order poles.

关键词： Euler's differential equation Meijer's G-function generalized hypergeometric functions Strongly singular coefficients

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On a theorem of T.!Gneiting on α-symmetric multivariate characteristic functions

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JOURNAL OF MULTIVARIATE ANALYSIS 2000年第2期75卷 269-278页

作者： Castell, WZ Univ Erlangen Nurnberg Erlangen Germany

*** (1998, J. Multivariate Analysis 64, 131-147) proved a relation between the primitives of the classes Phi (d)(2) and Phi (d)(1) of 2- and 1-symmetric characteristic functions on R-d, respectively. We will give a straightforward proof of his relation, answering a question of his. To do this we use the calculus of generalized hypergeometric functions. (C) 2000 Academic Press.

关键词： generalized hypergeometric functions alpha-symmetric characteristic functions norm-dependent positive definite functions

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Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

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NUCLEAR PHYSICS B 2008年第3期789卷 525-551页

作者： Bervillier, C. Boisseau, B. Giacomini, H. Univ Tours Lab Math & Phys Theor CNRS UMR 6083 F-37200 Tours France

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail). (c) 2007 Elsevier B.V. All rights reserved.

关键词： exact renormalization group derivative expansion critical exponents two-point boundary value problem generalized hypergeometric functions

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