Multivariate Fibonacci Polynomials of Order K and the Multiparameter Negative Binomial Distribution of the Same Order
Multivariate Fibonacci Polynomials of Order K and the Multiparameter Negative Binomial Distribution of the Same Order
复制标题
K阶多元斐波那契多项式及同阶多参数负二项分布
DOI：
10.1007/978-94-009-1910-5_30
复制
发表时间：
1990
期刊：
影响因子：
--
通讯作者：
Demetris L. Antzoulakos
中科院分区：
文献类型：
--
作者：
Andreas N. Philippou;Demetris L. Antzoulakos
除非另有明确说明，本文中k、r为固定正整数，n、ni（1≤i≤k）为规定的非负整数，p、qi（1≤i≤k）为区间（0,1）内满足关系p+q1+…+qk=1的实数，x、xi（1≤i≤k）为区间（0,∞）内的实数。设{Fn(k)(x)}n∞为k阶fibonacci型多项式的序列，即F0(k)(x)=0, F1(k)(x)=1 $$F_n^{\left( k \right)}\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\sum\limits_{i = 1}^n {F_{n - i}^{\left( k \right)}\left( x \right)} if 2 \leqslant n \leqslant k + 1,} \\ {x\sum\limits_{i = 1}^k {F_{n - i}^{\left( k \right)}\left( x \right)} if n \geqslant k + 2.} \end{array}} \right.$$
Unless otherwise explicitly stated, in this paper k and r are fixed positive integers, n and ni(1≤i≤k) are non-negative integers as specified, p and qi(1≤i≤k) are real numbers in the interval (0,1) which satisfy the relation p+q1+…+qk=1, and x and xi(1≤i≤k) are real numbers in the interval (0,∞). Let {Fn(k)(x)}n∞be the sequence of Fibonacci-type polynomials of order k, i.e. F0(k)(x)=0, F1(k)(x)=1, and $$F_n^{\left( k \right)}\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\sum\limits_{i = 1}^n {F_{n - i}^{\left( k \right)}\left( x \right)} if 2 \leqslant n \leqslant k + 1,} \\ {x\sum\limits_{i = 1}^k {F_{n - i}^{\left( k \right)}\left( x \right)} if n \geqslant k + 2.} \end{array}} \right.$$