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Existence and Regularity of Solution to the Generalized Tricomi Equation with a Singular Initial Datum at a Point

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Acta Mathematica Sinica,English Series 2012年第6期28卷 1135-1154页

作者： Kang Qun ZHANG Department of Mathematics&IMS Nanjing University

In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type initial datum on the degenerate plane is smooth away from the origin, domain. We suppose that an and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity.

关键词： Generalized Tricomi equation confluent hypergeometric function existence conormalregularity cusp singularity

Commuting Toeplitz Operators on Fock-Sobolev Spaces of Negative Orders

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Acta Mathematica Sinica,English Series 2023年第10期39卷 1989-2005页

作者： Hong Rae CHO Han-Wool LEE Department of Mathematics Pusan National UniversityBusan 46241Korea

In the setting of Fock-Sobolev spaces of positive orders over the complex plane,Choe and Yang showed that if the one of the symbols of two commuting Toeplitz operators with bounded symbols is non-trivially radial,then the other must also be *** this paper,we extend this result to the Fock-Sobolev space of negative order using the Fock-type space with a confluent hyper geometric function.

关键词： Fock–Sobolev spaces commutator of Toeplitz operators Mellin Transform confluent hypergeometric function

Some Representations of Unified Voigt functions

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Acta Mathematica Sinica,English Series 2005年第4期21卷 865-868页

作者： M.KAMARUJJAMA DineshSINGH Department of Applied Mathematics Z.H.College of Engg.and Tech.Aligarh Muslim UniversityAligarh-202002India

The authors derive a set of unified representations of the Voigt functions in terms of familiar special functions of Mathematical Physics. Some deductions from these representations are also considered.

关键词： Voigt functions Bessel functions confluent hypergeometric function Laguerre and Hermite polynomials

The calculating formula for radial matrix elements of a relativistic harmonic oscillator

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Chinese Physics B 2003年第8期12卷 831-835页

作者：强稳朝 FacultyofScience Xi'anUniversityofArchitectureandTechnologyXi’an710055China

A universal practical formula is given for calculating an integral which includes two confluent hypergeometric functions, power and exponential functions; then by means of this formula, the expressions of the radial m... 详细信息

关键词： relativistic harmonic oscillator radiial matrix element confluent hypergeometric function

Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions

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Advances in Pure Mathematics 2020年第7期10卷 371-392页

作者： Victor Nijimbere School of Mathematics and Statistics Carleton University Ottawa ON Canada

The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, and where α,η and β are real or complex constants are evaluated in terms of the confluent hypergeometric function 1F1 and the hypergeometric function 1F2. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions 1F1 and 1F2. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (x2) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.

关键词： Non-Elementary Integrals hypergeometric function confluent hypergeometric function Probability Measure Generalized Gamma-Type Distributions Generalized Gaussian-Type Distributions

Solution of the Dirac equation with the ring-shaped oscillator potential

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Journal of Chongqing University 2008年第2期7卷 141-144页

作者：张爱萍 Science College Xi'an University of Architecture and Technology

The ring-shaped oscillator potential, obtained by replacing the Coulomb part of the Hartmann potential by a harmonic oscillator term, was investigated. Under the equal vector potential and scalar potential, the Dirac equation was solved in spherical coordinate. The exact energy spectrum of the bound states was presented as a solution to the confluent hypergeometric equation by boundary conditions. Furthermore, the normalized angular and radial wave functions were presented.

关键词： ring-shaped oscillator bound solution Dirac equation confluent hypergeometric function