检索结果-内蒙古大学图书馆

Fast and stable rational approximation of generalized hypergeometric functions

NUMERICAL ALGORITHMS 2025年第2期98卷 587-624页

作者： Slevinsky, Richard Mikael Univ Manitoba Dept Math Winnipeg MB Canada

Rational approximations of generalized hypergeometric functions pFq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_pF_q$$\end{document} of type (n+k,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+k,k)$$\end{document} are constructed by the Drummond and factorial Levin-type sequence transformations. We derive recurrence relations for these rational approximations that require O[max{p,q}(n+k)]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}[\max \{p,q\}(n+k)]$$\end{document} flops. These recurrence relations come in two forms: for the successive numerators and denominators;and, for an auxiliary rational sequence and the rational approximations themselves. Numerical evidence suggests that these recurrence relations are much more stable than the original formul AE for the Drummond and factorial Levin-type sequence transformations. Theoretical results on the placement of the poles of both transformations confirm the superiority of factorial Levin-type transformation over the Drummond transformation.

关键词： generalized hypergeometric functions Drummond sequence transformation Factorial Levin-type sequence transformation

来源：评论

学校读者我要写书评

暂无评论

generalized hypergeometric functions associated with k-uniformly convex functions

引用

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2002年第12期44卷 1515-1526页

作者： Gangadharan, A Shanmugam, TN Srivastava, HM Sri Venkateswara Coll Engn Dept Math & Comp Applicat Tamil Nadu 602205 India Anna Univ Sch Math Madras 600025 Tamil Nadu India Univ Victoria Dept Math & Stat Victoria BC V8W 3P4 Canada

For a certain linear operator which is defined by means of the Hadamard product (or convolution) with a generalized hypergeometric function, the authors aim at investigating various mapping and inclusion properties involving such subclasses, of analytic and univalent functions as (for example) k-uniformly convex functions and k-starlike functions. Relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： analytic functions univalent functions generalized hypergeometric functions Hadamard product (or convolution) linear operators k-uniformly convex functions k-starlike functions parabolic starlike functions mapping and inclusion properties coefficient inequalities fractional calculus operators Gauss summation theorem

来源：评论

学校读者我要写书评

暂无评论

generalized hypergeometric functions and exact distributions of test statistics

引用

American Journal of Mathematical and Management Sciences 1989年第1-2期9卷 155-175页

作者： Rathie, P.N. Institute of Mathematics Statistics and Computer Science State University of Campinas Campinas S.P. 13081 Ca.ixa Postal 6065 Brazil

In this review article, an attempt has been made to give an up-to-date survey of the work done on the applications of generalized hypergeometric functions (especially G, H and R functions) to the exact distributions of test statistics. No attempt has been made to include details on the work connected with zonal polynomials, characteristic roots or asymptotic distributions. © 1989 by American Sciences Press, Inc.

关键词： Exact distributions of test statistics G and H-functions generalized hypergeometric functions

来源：评论

学校读者我要写书评

暂无评论

HYPERDIRE-hypergeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function F_C of three variables

引用

COMPUTER PHYSICS COMMUNICATIONS 2016年 206卷 78-83页

作者： Bytev, Vladimir V. Kniehl, Bernd A. Univ Hamburg Inst Theoret Phys 2 D-22761 Hamburg Germany Joint Inst Nucl Res Dubna 141980 Moscow Region Russia

We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function F-C of three variables. Program summary Program title: HYPERDIRE Catalogue identifier: AEPP_v4_0 Program summary URL: http://***/summaries/AEPP_v4_*** Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 243461 No. of bytes in distributed program, including test data, etc.: 61610782 Distribution format: *** Programming language: Mathematica. Computer: All computers running Mathematica. Classification: 4.4. Does the new version supersede the previous version?: No, it significantly extends the previous version. Nature of problem: Reduction of hypergeometric function F-C of three variables to a set of basis functions. Solution method: Differential reduction. Reasons for new version: The extension package allows the user to handle the Lauricella function F-C of three variables. Summary of revisions: The previous version goes unchanged. Running time: Depends on the complexity of the problem. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Feynman integrals generalized hypergeometric functions Differential reduction

来源：评论

学校读者我要写书评

暂无评论

Pearson equations for discrete orthogonal polynomials: I. generalized hypergeometric functions and Toda equations

引用

STUDIES IN APPLIED MATHEMATICS 2022年第3期148卷 1141-1179页

作者： Manas, Manuel Fernandez-Irisarri, Itsaso Gonzalez-Hernandez, Omar F. Univ Complutense Madrid Dept Fis Teor Plaza Ciencias 1 Madrid 28040 Spain Inst Ciencias Matemat ICMAT Campus Cantoblanco UAM Madrid 28049 Spain

The Cholesky factorization of the moment matrix is applied to discrete orthogonal polynomials on the homogeneous lattice. In particular, semiclassical discrete orthogonal polynomials, which are built in terms of a discrete Pearson equation, are studied. The Laguerre-Freud structure semiinfinite matrix that models the shifts by +/- 1 in the independent variable of the set of orthogonal polynomials is introduced. In the semiclassical case it is proven that this Laguerre-Freud matrix is banded. From the well-known fact that moments of the semiclassical weights are logarithmic derivatives of generalized hypergeometric functions, it is shown how the contiguous relations for these hypergeometric functions translate as symmetries for the corresponding moment matrix. It is found that the 3D Nijhoff-Capel discrete Toda lattice describes the corresponding contiguous shifts for the squared norms of the orthogonal polynomials. The continuous 1D Toda equation for these semiclassical discrete orthogonal polynomials is discussed and the compatibility equations are derived. It is also shown that the Kadomtesev-Petviashvilii equation is connected to an adequate deformed semiclassical discrete weight, but in this case, the deformation does not satisfy a Pearson equation.

关键词： 3D Nijhoff-Capel discrete Toda equation Cholesky factorization contigous relations discrete orthogonal polynomials generalized hypergeometric functions Pearson equations Toda hierarchy

来源：评论

学校读者我要写书评

暂无评论

On the Mellin transform of products of Bessel and generalized hypergeometric functions

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1997年第2期85卷 271-286页

作者： Miller, AR 1616 Eighteenth Street NW Washington DC 20009-2530 USA

We deduce in an elementary way representations for the Mellin transform of a product of Bessel functions F-0(1)[-a(2)x(2)] and generalized hypergeometric functions F-p(p+1)[-b(2)x(2)] for a,b > 0. As a corollary we obtain a transformation formula for F-p+1(p)[1] which was discovered by Wimp in 1987 by using Bailey's method for the specialization F-3(2)[1].

关键词： generalized hypergeometric functions Mellin transforms

来源：评论

学校读者我要写书评

暂无评论

Inductance Calculations for Circular Coils With Rectangular Cross Section and Parallel Axes Using Inverse Mellin Transform and generalized hypergeometric functions

引用

IEEE TRANSACTIONS ON POWER ELECTRONICS 2017年第2期32卷 1367-1374页

作者： Luo, Yao Wang, Xiaowei Zhou, Xinglong Wuhan Univ Sch Elect Engn Wuhan 430072 Peoples R China South Cent Univ Nationalities Coll Elect & Informat Wuhan 430074 Peoples R China

The inductance integrals of air-core circular coils with rectangular cross section and parallel axes are difficult to tackle with analytical method due to the inclusion of Struve functions. Using the inverse Mellin transform, these Bessel-Struve integrals will be continued analytically to the complex plane, and then by virtue of contour deformation and residue theorem, they can be expanded to the series containing the generalized hypergeometric functions which are easy to execute in common mathematical software packages. The series solutions are preferable in case the difficulties arise in the evaluations of Bessel-Struve integrals, though they do not cover the whole region of coil geometric parameters. In addition, the obtained series were compared numerically with the corresponding integrals, complete consistency was shown clearly. By means of the proposed method, the computation efficiency can be improved by several orders of magnitude compared to that of the corresponding integral methods.

关键词： generalized hypergeometric functions inductance calculations inverse mellin transform residue theorem

来源：评论

学校读者我要写书评

暂无评论

Acceleration of generalized hypergeometric functions through precise remainder asymptotics

引用

NUMERICAL ALGORITHMS 2012年第3期59卷 447-485页

作者： Willis, Joshua L. Abilene Christian Univ Dept Phys Abilene TX 79699 USA Max Planck Inst Gravitat Phys D-30167 Hannover Germany

We express the asymptotics of the remainders of the partial sums {s (n) } of the generalized hypergeometric function q + 1 Fq ((alpha 1, ... , alpha q+1)(beta 1, ... , beta q) vertical bar z through an inverse power series z(n)n(lambda) Sigma c(k)/n(k), where the exponent lambda and the asymptotic coefficients {c(k)} may be recursively computed to any desired order from the hypergeometric parameters and argument. From this we derive a new series acceleration technique that can be applied to any such function, even with complex parameters and at the branch point z = 1. For moderate parameters (up to approximately ten) a C implementation at fixed precision is very effective at computing these functions;for larger parameters an implementation in higher than machine precision would be needed. Even for larger parameters, however, our C implementation is able to correctly determine whether or not it has converged;and when it converges, its estimate of its error is accurate.

关键词： generalized hypergeometric functions Series acceleration Recurrence asymptotics

来源：评论

学校读者我要写书评

暂无评论

Convolution of Harmonic Mappings On The Exterior Unit Disk and the generalized hypergeometric functions

引用

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN 2011年第2期18卷 239-251页

作者： Ali, Rosihan M. Stephen, B. Adolf Subramanian, K. G. Lee, S. K. Univ Sains Malaysia Sch Math Sci Usm Penang 11800 Malaysia Madras Christian Coll Dept Math Madras 600059 Tamil Nadu India

A new class is introduced consisting of harmonic univalent functions on the exterior unit disk defined by convolution. This class generates several known and new subclasses of harmonic univalent functions as special cases. A necessary and sufficient convolution condition is obtained for functions to belong to the class. A corresponding general class of harmonic functions with negative coefficients is also introduced, and coefficient condition that is both necessary and sufficient is obtained for the class. Extreme points are also determined. As applications, starlikeness conditions of the Liu-Srivastava linear operator involving the generalized hypergeometric functions are discussed.

关键词： Harmonic functions convolution harmonic starlike and convex functions negative coefficients Liu-Srivastava operator generalized hypergeometric functions

来源：评论

学校读者我要写书评

暂无评论

Lp-bounded operators involving generalized hypergeometric functions

引用

INTEGRAL TRANSFORMS AND SPECIAL functions 2011年第2期22卷 143-149页

作者： Habibullah, G. M. Mubeen, S. Natl Coll Business Adm & Econ Lahore Pakistan

We herein determine an integral representation of generalized hypergeometric functions mFm extending the usual results on 1F1. After formulating integral operators involving the generalized hypergeometric functions of the form: [image omitted] and [image omitted] we prove that these operators are composition of generalized variants of the Laplace transform (and Watson) and Erdelyi-Kober fractional integral operators. We also prove that these operators are bounded in Lp.

关键词： fractional integral transforms Liouville and Kober fractional integrals generalized hypergeometric functions integral transforms with generalized hypergeometric functions in the kernel

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：