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On Schwarzian Triangle functions, Automorphic Forms and a Generalization of Ramanujan’s Triple Differential Equations

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Acta Mathematica Sinica,English Series 2018年第11期34卷 1648-1662页

作者： Li Chien SHEN Department of Mathematics University of Florida

Let G be the group of the fractional linear transformations generated by T（τ）=τ ＋ λ, S（τ）=（τ cos π/n ＋ sin π/n）/（-τ sin π/n ＋ cos π/n）;where λ=2（cos π/m ＋ cos π/n）/sin π/n;m, n is a pair of integers with either n ≥ 2, m ≥ 3 or n ≥ 3, m ≥ 2; τ lies in the upper half plane H.A fundamental set of functions f0, fi and f∞ automorphic with respect to G will be constructed from the conformal mapping of the fundamental domain of G. We derive an analogue of Ramanujan＇s triple differential equations associated with the group G and establish the connection of f0, fi and f∞ with a family of hypergeometric functions.

关键词： hypergeometric function Schwarzian triangle function Jacobi theta functions Ramanu-jan＇s triple differential equations

THE SPHERICAL functionS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

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Acta Mathematica Scientia 2007年第4期27卷 867-874页

作者：杨乔华张钦 Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071China School of Mathematics and Statistics Wuhan University Wuhan 430072China

Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.

关键词： Spherical function central limit theorem hypergeometric function

AN ANALYTICAL SOLUTION FOR AN EXPONENTIAL- TYPE DISPERSION PROCESS

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Applied Mathematics and Mechanics(English Edition) 2001年第3期22卷 368-371页

作者： WANG Zi-ting(王子亭) Department of Applied Mathematics University of PetroleumDongying 257062 P R China

The dispersion process in heterogeneous porous media is distance-dependent, which results from multi-scaling property of heterogeneous structure. An analytical model describing the dispersion with an exponential dispersion function is built, which is transformed into ODE problem with variable coefficients, and obtained analytical solution for two type boundary conditions using hypergeometric function and inversion technique. According to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed

关键词： heterogeneous porous media dispersion hypergeometric function analytical solution

An Explicit Solution for a Series and Parallel Queue with Retrial,Losses,and Bernoulli Schedule

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Journal of the Operations Research Society of China 2016年第1期4卷 121-129页

作者： Shi-Zhong Zhou Li-Wei Liu Jian-Jun Li Department of Statistics and Financial Mathematics School of ScienceNanjing University of Science and TechnologyNanjing 210094China

This paper deals with the series and parallel queueing system in which there are two servers whose service time follow two exponential distributions.Each arriving customer either enters into the tandem service with probability or joins the service of the single server with complementary probability.We assume that the customers of arriving at the first server who find the first server is busy join an orbit and retry to enter the server after some time and of arriving at the second server who find the second server is busy are lost.For this model,we obtain the explicit expressions of the joint stationary distribution between the number of customers in the orbit and the states of the servers.

关键词： Series and parallel queue Retrial Bernoulli schedule Explicit solution hypergeometric function

Modified Double Zeta function and Its Properties

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Advances in Pure Mathematics 2016年第3期6卷 159-167页

作者： Arif M. Khan Department of Mathematics Jodhpur Institute of Engineering & Technology Jodhpur India

The present paper aims at introducing and investigating a new class of generalized double zeta function i.e. modified double zeta function which involves the Riemann, Hurwitz, Hurwitz-Lerch, Barnes double zeta function and Bin-Saad generalized double zeta function as particular cases. The results are obtained by suitably applying Riemann-Liouville type and Tremblay fractional integral and differential operators. We derive the expansion formula for the proposed function with some of its properties via fractional operators and discuss the link with known results.

关键词： Modified Zeta function Riemann-Liouville Operator Tremblay Fractional Operators hypergeometric function

Fekete-Szego Problem for a Subclass of Meromorphic functions Defined by the Dziok-Srivastava Operator

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Communications in Mathematical Research 2018年第2期34卷 184-192页

作者： Guo Dong Li Zong-tao Xiong Liang-peng Foundation Department Chuzhou Vocational and Technical CollegeChuzhouAnhui239000 Foundation Department Guangzhou Civil Aviation CollegeGuangzhou510403 School of Mathematics and Statistics Wuhan UniversityWuhan430072

By using the hypergeometric function defined by the Dziok-Srivastava operator, a new subclass of meromorphic function is introdued. We obtain Fekete-Szeg? inequalities for the meromorphic function f(z) for which α-(1... 详细信息

关键词： analytic and meromorphic function starlike and convex function hypergeometric function Fekete-Szeg? problem Dziok-Srivastava operator Hadamard product

Exact bound state solutions of the Klein-Gordon particle in Hulthn potential

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Chinese Physics B 2008年第9期17卷 3214-3216页

作者：张民仓 College of Physics and Information Technology Shaanxi Normal University

In this paper, the Klein-Gordon equation with the spherical symmetric Hulthén potential is turned into a hypergeometric equation and is solved in the framework of function analysis exactly. The corresponding bound state solutions are expressed in terms of the hypergeometric function, and the energy spectrum of the bound states is obtained as a solution to a given equation by boundary constraints.

关键词： Hulthén potential Klein-Gordon equation bound state hypergeometric function

ASYMPTOTIC EXPANSION AND ESTIMATE OF THE LANDAU CONSTANT

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Analysis in Theory and Applications 2001年第4期17卷 58-64页

作者： A.Eisinberg G.Franzè N.Salerno DEIS Università della CalabriaItaly

Properties of Landau constant are investigated in this note. A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized. Moreover, we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.

关键词： asymptotic expansion hypergeometric function

CERTAIN SUBCLASS OF p-VALENT MEROMORPHIC ANALYTIC functionS INVOLVING CERTAIN INTEGRAL OPERATOR

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Analysis in Theory and Applications 2012年第4期28卷 312-320页

作者： M.K. Aouf T.M. Seoudy Mansoura University Fayoum University

The purpose of the present paper is to introduce a new subclass of p-valent meromorphic functions by using certain integral operator and to investigate various properties for this subclass.

关键词： analytic function meromorphic function hypergeometric function linear op-erator