The general solution of (5. 122) is an arbitrary linear combination of a series of even powers and a series of odd powers.
是一个偶次幂级数和一个奇次幂级数的任意线性组合。The process of replacing polynomials by formal power series is an example of a general device known as completion.
用形式幂级数来代替多项式的过程是被称之为完备化的这种一般手段的一个例子。By constructing a convergent power series solution of an auxiliary equation, analytic solutions for the original equation are obtained.
讨论了一阶迭代微分方程解析解的存在性，通过构造一个辅助方程的幂级数解给出该方程的解析解。Power series, radius of convergence; function that can be expanded in a power series on an interval.
幂级数；收敛半径；可展开为幂级数的函数。The expression of relative distortion based on even-power series of a radial radius is commonly used in camera calibration.
基于径向半径偶次幂级数的相对畸变表达式在相机校准中被广泛地采用。In this thesis we discuss the filtration dimensions and tilting modules of generalized power series algebras.
本文研究了广义幂级数代数的滤链维数与倾斜模。Secondly, by using the stretched variable and the expanding theory of power series, the initial layer term of solution was constructed.
其次，利用伸长变量和幂级数展开理论，构造了解的初始层项。Furthermore, we give a class of identities for power series of Lie type and some partition theorems.
同时给出了一系列的李型幂级数恒等式和一些整数分划定理。For the corrugated parts, the accurate solution for the perturbation of different orders can not be obtained.
对于波纹部分，不能直接得到各阶摄动的精确解，采用幂级数方法求解。