1) recursively defined sequence
递归定义的序列
2) recursive sequence
递归序列
1.
The relation between the iteration of projective function and the linear recursive sequences of order 2 is given.
先给出射影函数的迭代与 2阶线性递归序列的关系 ,进而得到此递归序列与Bernoulli数的一个恒等
3) recurrent sequence
递归序列
1.
This paper proves that the Diophantine equation has only integer solution with the help of the Pell method taking an integer>1 as module to make inconsistency,the natures of recurrent sequences and equivalent Pell equation.
采用对方程取某个正整数M>1为模来制造矛盾的同余法和利用递归序列的性质,以及Pell方程的性质,证明不定方程x3-1=13y2仅有整数解(x,y)=(1,0)。
2.
In this paper,the author has proved, with two method of contradictor recurrent sequences and congruence when modules of some positive integer M>1, that the Diophantine equation x~3+1=19y~2 has only integer solution(x,y)=(1,0).
利用两种初等的方法,即对方程取某个正整数M>1为模来制造矛盾的同余法和递归序列法,证明了不定方程x3 -1=19y2 仅有整数解(x,y)=(1,0),从而进一步的证明了方程x2 -19y2 =-13无整数解;方程x2 -3r2 =-3仅有整数解(1。
3.
With the method of recurrent sequence and congruences,proved that the Diophantine equation x3+1 =37y2has only integer solution(x,y)=(-1,0),(11,±6).
利用递归序列,同余式证明了丢番图方程x 3+1=37y2,仅有整数解(x,y)=(-1,0),(11,±6)。
4) recurrence sequences
递归序列
1.
Formulas for simple and direct computations for Euler--Bernoulli polynomials of n variablesare presented,some identities containing recurrence sequences and Euler--Bernooulli polynomials of n variables have been established.
给出简捷计算n元Euler-Bernoulli多项式的公式，建立一些包含递归序列和上述多项式的恒等式。
5) recurrence sequence
递归序列
1.
In this paper using the method of recurrence sequences we show that there does not exist positive solution in the equation of the title.
证明过程中仅涉及到了初等的数论知识,就是采用了递归序列的方法,证明了不定方程x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3)无正整数解,同时这个证明过程也给出了这个不定方程组的全部整数解,它们是(x,y)=(-3,0),(-3,-1),(-3,-2),(-3,-3),(-2,0),(-2,-1),(-2,-2),(-2,-3),(-1,0),(-1,-1),(-1,-2),(-1,-3),(0,0),(0,-1),(0,-2),(0,-3)。
2.
In this paper the author gives a general expression and the property of a 3degreelinear recurrence sequence by using Jordan s normal form of the coefficient matrix.
用3阶线性递归序列的系数矩阵的若当标准形,给出了3阶线性递归序列的通项及一个性质。
3.
Some identities involving recurrence sequences and higher order multivariable Nrlund Euler_Bernoulli polynomials are established.
给出了高阶多元N rlundEuler多项式和高阶多元N rlundBernoulli多项式的定义,讨论了它们的一些重要性质,建立了一些包含递归序列和上述多项式的恒等式·
6) recursive definition of function
函数的递归定义
补充资料：递归定义
递归定义
recursive definition
递归定义fre恤幽e defi面匕on;pe‘，pc皿二oeonpe及e加-H”el (数学中)经常使用的定义函数的方式，用此方式在一给定点寻求的函数值用(给定的适当前趋关系下)前面点的值来定义.数论函数的递归定义是算法(见递归(recursion))理沦研究的主题.在集合论中递归定义被经常用来以超限递归(tmns俪te reCurslon)，定义序数上的函数.在更大的范围内，在可允许集合理沦中递归定义被研究.在它的基础上综合了集合论与算法论的思想(见12」).
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参考词条