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THE ASYMPTOTIC SOLUTION OF LINEAR SECOND ORDER DIFFERENTIAL EQUATIONS IN A DOMAIN CONTAINING A TURNING POINT AND REGULAR SINGULARITY THE ASYMPTOTIC EXPANSION OF LEGENDRE FUNCTIONS OF LARGE DEGREE AND ORDER

机译：具有转动点和正则奇异性的一个区域中线性二阶微分方程的渐近解 - 大阶和阶数的LEGENDRE函数的渐近展开

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The point z=0 is a regular singularity of the equation and a branch-cut extending from z=0 is taken through the point z=z0 which is assumed to lie on the positive real z-axis. Asymptotic expansions for the solutions of the equation, valid uniformly with respect to z in domains including z=0, z=z0 ± i. O, are derived in terms of Bessel functions of large order.

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R. C. THORNE;
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年度 1956
页码 1-73
总页数 73
原文格式 PDF
正文语种 eng
中图分类工业技术;
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专利

1. On the asymptotic expansions of numerical solutions to second order differential equations with a regular singular point [J] . Weiss R., Anderssen RS., de Hoog FR. Mathematical models and methods in applied sciences . 2001,第1期

机译：具有正则奇异点的二阶微分方程数值解的渐近展开
2. Asymptotic solution of differential equations in a domain containing a regular singular point [J] . N. D. Kazarinoff, R. McKelvey Canadian Journal of Mathematics . 1956,第1956期

机译：包含正则奇异点的域中微分方程的渐近解
3. ASYMPTOTICS OF RAPIDLY VARYING SOLUTIONS OF DIFFERENTIAL EQUATIONS ASYMPTOTICALLY CLOSE TO EQUATIONS WITH REGULARLY VARYING NONLINEARITIES [J] . V. M. Evtukhov, A. V. Drozhzhina Journal of Mathematical Sciences . 2021,第2期

机译：渐近方程迅速改变差异靠近方程式循环方程迅速变化的差异性，具有规则不同的非线性
4. Almost periodic and asymptotically almost periodic mild solutions for nonlinear abstract functional differential equations with infinite delay [C] . Peng Xiao, Yanfei Du 2011 International Conference on Multimedia Technology . 2011

机译：无限时滞非线性抽象泛函微分方程的概周期解和渐近概周期解
5. Asymptotic expansions of the regular solutions to the three-dimensional Navier-Stokes equations and applications to the analysis of the helicity. [D] . Hoang, Luan Thach. 2005

机译：三维Navier-Stokes方程正则解的渐近展开及其在螺旋度分析中的应用。
6. Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy–Sobolev exponent and singular nonlinearity [O] . Liejun Shen -1

机译：具有Hardy-Sobolev指数和奇异非线性的Kirchhoff型方程解的多重性和渐近性
7. Asymptotic expansion of singular solutions and characteristic polygon of linear partial differential equations with holomorphic coefficients (Microlocal Analysis and PDE in the Complex Domain) [O] . Ouchi Sunao 2000

机译：含全纯系数的线性偏微分方程的奇异解和特征多边形的渐近展开（复域中的微局部分析和PDE）
8. ASYMPTOTIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH A REGULAR SINGULAR POINT [R] . K. G. Guderley 1959

机译：具有正则奇异点的微分方程的渐近解

THE ASYMPTOTIC SOLUTION OF LINEAR SECOND ORDER DIFFERENTIAL EQUATIONS IN A DOMAIN CONTAINING A TURNING POINT AND REGULAR SINGULARITY THE ASYMPTOTIC EXPANSION OF LEGENDRE FUNCTIONS OF LARGE DEGREE AND ORDER

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