Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds t...Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.展开更多
Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurati...Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.展开更多
In this paper, some Wgh inequalities for univalent harmonic analytic functions defined by Wright's generalized hypergeometric (Wgh) functions to be in certain classes are observed and proved. Some consequent resul...In this paper, some Wgh inequalities for univalent harmonic analytic functions defined by Wright's generalized hypergeometric (Wgh) functions to be in certain classes are observed and proved. Some consequent results are also discussed.展开更多
This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe...This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe de Feriets series of double hypergeometric series F;.展开更多
文摘Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.
文摘Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.
文摘圆盘线圈是近年来兴起的无线能量传输系统中能量耦合的核心元件。通过引入广义超几何函数pFq 将圆盘线圈的自感积分表达式化为闭式。类似地,通过建立完全椭圆积分与广义超几何函数之间的联系将同轴共面圆盘线圈的互感化为闭式。这些闭式解使上述电感计算问题不再需要数值积分。进一步,基于所得闭式解,分析了圆盘线圈的GPW(given piece of wire)优化问题,得到了给定导线所能绕制的圆盘线圈自感最大值,且达到最大值的圆盘线圈外半径与内半径之比是一个与导线几何参数无关的常数。数值计算表明所得公式与已有方法所得结果一致性较好。
文摘In this paper, some Wgh inequalities for univalent harmonic analytic functions defined by Wright's generalized hypergeometric (Wgh) functions to be in certain classes are observed and proved. Some consequent results are also discussed.
文摘This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe de Feriets series of double hypergeometric series F;.
