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Chinese Physics B 2014年第8期23卷 246-251页

作者：范洪义王震 Department of Physics Ningbo University College of Science Changzhou Institute of Technology

For directly normalizing the photon non-Gaussian states （e.g., photon added and subtracted squeezed states）, we use the method of integration within an ordered product （IWOP） of operators to derive some new bosonic operator-ordering identities. We also derive some new integration transformation formulas about one- and two-variable hermite polynomials in complex function space. These operator identities and associative integration formulas provide much convenience for constructing non-Gaussian states in quantum engineering.

关键词： IWOP method squeezed states hermite polynomials

A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE hermite polynomials

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Acta Mathematica Scientia 2008年第4期28卷 834-842页

作者：史薇 School of Mathematics and Statistics Wuhan University

In this article,the author extends the validity of a uniform asymptotic expansion of the hermite polynomials Hn（√2n＋1α）to include all positive values of α. His method makes use of the rational functions introduc... 详细信息

关键词： hermite polynomials uniform asymptotic expansion Airy function

Asymptotic Approximations of Apostol-Tangent polynomials in Terms of Hyperbolic Functions

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Computer Modeling in Engineering & Sciences 2022年第7期131卷 133-151页

作者： Cristina B.Corcino Wilson D.Castaneda Jr Roberto B.Corcino Research Institute for Computational Mathematics and Physics Cebu Normal UniversityCebu City6000Philippines Mathematics Department Cebu Normal UniversityCebu City6000Philippines Department of Mathematics Cebu Technological UniversityCebu City6000Philippines

The tangent polynomials Tn(z)are generalization of tangent numbers or the Euler zigzag numbers *** particular,Tn(0)=*** polynomials are closely related to Bernoulli,Euler and Genocchi *** of the extensions and analogues of special polynomials that attract the attention of several mathematicians is the Apostol-type *** of these Apostol-type polynomials is the Apostol-tangent polynomials Tn(z,λ).Whenλ=1,Tn(z,1)=Tn(z).The use of hyperbolic functions to derive asymptotic approximations of polynomials together with saddle point method was applied to the Bernoulli and Euler polynomials by Lopez and *** same method was applied to the Genocchi polynomials by Corcino et *** essential steps in applying the method are(1)to obtain the integral representation of the polynomials under study using their exponential generating functions and the Cauchy integral formula,and(2)to apply the saddle point *** is found out that the method is applicable to Apostol-tangent *** a result,asymptotic approximation of Apostol-tangent polynomials in terms of hyperbolic functions are derived for large values of the parameter n and uniform approximation with enlarged region of validity are also ***,higher-order Apostol-tangent polynomials are *** the same method,asymptotic approximation of higherorder Apostol-tangent polynomials in terms of hyperbolic functions are derived and uniform approximation with enlarged region of validity are also *** is important to note that the consideration of Apostol-type polynomials and higher order Apostol-type polynomials were not done by Lopez and *** part is first done in this *** accuracy of the approximations are illustrated by plotting the graphs of the exact values of the Apostol-tangent and higher-order Apostol-tangent polynomials and their corresponding approximate values for specific values of the parameters n,λand m.

关键词： Apostol-tangent polynomials tangent polynomials Genocchi polynomials hermite polynomials asymptotic approximation

Large time asymptotics for solutions to a nonhomogeneous Burgers equation

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Applied Mathematics and Mechanics(English Edition) 2010年第9期31卷 1189-1196页

作者： S.R.CHIDELLA M.K.YADAV Department of Mathematics Indian Institute of Technology Madras

In this article, the solutions to a nonhomogeneous Burgers equation subject to bounded and compactly supported initial profiles are constructed. In an interesting study, Kloosterziel （Journal of Engineering Mathematics 24, 213-236 （1990）） represented a solution to an initial value problem （IVP） for the heat equation, with an initial data in a class of rapidly decaying functions, as a series of self-similar solutions to the heat equation. This approach quickly revealed the large time behaviour for the solution to the IVP. Inspired by Kloosterziel＇s approach, the solution to the nonhomogeneous Burgers equation is expressed in terms of the self-similar solutions to the heat equation. The large time behaviour of the solutions to the nonhomogeneous Burgers equation is obtained.

关键词： nonhomogeneous Burgers equation hermite polynomials self-similar solutions

Solving Fractional Integro-Differential Equations by Using Sumudu Transform Method and hermite Spectral Collocation Method

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Computers, Materials & Continua 2018年第2期54卷 161-180页

作者： Y.A.Amer A.M.S.Mahdy E.S.M.Youssef Department of Mathematics Faculty of Science44519Zagazig UniversityEgypt Department of Mathematics and Statistics Faculty of ScienceTaif UniversitySaudi Arabia

In this paper we are looking forward to finding the approximate analytical solutions for fractional integro-differential equations by using Sumudu transform method and hermite spectral collocation *** fractional derivatives are described in the Caputo *** applications related to Sumudu transform method and hermite spectral collocation method have been developed for differential equations to the extent of access to approximate analytical solutions of fractional integro-differential equations.

关键词： Caputo derivative integro-differential equations hermite polynomials sumudu transform

Duality between Bessel Functions and Chebyshev polynomials in Expansions of Functions

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Advances in Pure Mathematics 2023年第8期13卷 504-536页

作者： Alfred Wünsche Humboldt-Universitä t Berlin Institut für Physik Nichtklassische Strahlung (MPG) Berlin Germany

In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.

关键词： Spherical Bessel Functions Chebyshev polynomials Legendre polynomials hermite polynomials Derivatives of Delta Functions Normally and Anti-Normally Ordered Operators

Numerical studies for solving fractional integro-differential equations

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Journal of Ocean Engineering and Science 2018年第2期3卷 127-132页

作者： A.M.S.Mahdy Department of Mathematics Faculty of ScienceZagazig UniversityZagazigEgypt Department of Mathematics Faculty of ScienceTaif UniversitySaudi Arabia

In this paper,we give a new numerical method for solving a linear system of fractional integro-differential *** fractional derivative is considered in the Caputo *** proposed method is least squares method aid of hermite *** suggested method reduces this type of systems to the solution of systems of linear algebraic *** demonstrate the accuracy and applicability of the presented method some test examples are *** results show that this approach is easy to implement and accurate when applied to integro-differential *** show that the solutions approach to classical solutions as the order of the fractional derivatives approach.

关键词： Least squares method Caputo fractional hermite polynomials Linear fractional integro-differential equations

(0,1;0)-INTERPOLATION ON INFINITE INTERVAL(-∞,+∞)

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Analysis in Theory and Applications 2006年第2期22卷 105-113页

作者： Pankaj Mathur Lucknow University Lucknow

In this paper, we study the explicit representation and convergence of （0, 1;0）-interpolation on infisite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values areprescribed at two set of points namely the zeros of Hn（x） and H′n （x） and the first derivatives at the zerosof H′n（x）.

关键词： interpolation hermite polynomials convergence

Eigenfunctions for a Quantum Wire on a Single Electron at Its Surface and in the Quantum Well with Beaded Fractional Quantized States for the Fractional Charges

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Journal of Applied Mathematics and Physics 2016年第2期4卷 320-327页

作者： Saleem Iqbal Farhana Sarwar Syed Mohsin Raza Department of Mathematics University of Balochistan Quetta Pakistan Department of Mathematics F. G. Girls Degree College Quetta Pakistan Department of Physics University of Balochistan Quetta Pakistan

We developed energy profiles for the fractional quantized states both on the surface of electron due to overwhelming centrifugal potentials and inside the electron at different locations of the quantum well due to overwhelming attractive electrodynamic potentials. The charge as a physical constant and single entity is taken as density and segments on their respective sub-quanta (floats on sub quanta) and hence the fractional charge quantiz at in. There is an integrated oscillatory effect which ties all fractional quantized states both on the surface and in the interior of the volume of an electron. The eigenfunctions, i.e., the energy profiles for the electron show the shape of a string or a quantum wire in which fractional quantized states are beaded. We followed an entirely different approach and indeed thesis to reproducing the eigenfunctions for the fractional quantized states for a single electron. We produced very fascinating mathematical formulas for all such cases by using hermite and Laguerre polynomials, spherical based and Neumann functions and indeed asymptotic behavior of Bessel and Neumann functions. Our quantization theory is dealt in the momentum space.

关键词： Fractional Charge Quantization Fractional Fourier Transform hermite polynomials Sub Quanta of Electron Spherical Bessel and Neumann Functions Lagueree polynomials

A New Technique for Solving Fractional Order Systems: hermite Collocation Method

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Applied Mathematics 2016年第18期7卷 2307-2323页

作者： Nilay Akgonullu Pirim Fatma Ayaz Ankara Turkey Department of Mathematics Gazi University Ankara Turkey

In this study, we establish an approximate method which produces an approximate hermite polynomial solution to a system of fractional order differential equations with variable coefficients. At collocation points, this method converts the mentioned system into a matrix equation which corresponds to a system of linear equations with unknown hermite polynomial coefficients. Construction of the method on the aforementioned type of equations has been presented and tested on some numerical examples. Results related to the effectiveness and reliability of the method have been illustrated.

关键词： Fractional Order Differential Equations hermite polynomials hermite Series Collocation Methods