Multivariate Fibonacci Polynomials of Order K and the Multiparameter Negative Binomial Distribution of the Same Order

Andreas N. Philippou and Demetris L. Antzoulakos

A chapter in Applications of Fibonacci Numbers, 1990, pp 273-279 from Springer

Abstract: Abstract Unless otherwise explicitly stated, in this paper k and r are fixed positive integers, n and n i (1≤i≤k) are non-negative integers as specified, p and q i (1≤i≤k) are real numbers in the interval (0,1) which satisfy the relation p+q1+…+q k =1, and x and x i (1≤i≤k) are real numbers in the interval (0,∞). Let {F n (k) (x)} n ∞ be the sequence of Fibonacci-type polynomials of order k, i.e. F 0 (k) (x)=0, F 1 (k) (x)=1, and (1.1) $$F_n^{\left( k \right)}\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\sum\limits_{i = 1}^n {F_{n - i}^{\left( k \right)}\left( x \right)} if 2 \leqslant n \leqslant k + 1,} \\ {x\sum\limits_{i = 1}^k {F_{n - i}^{\left( k \right)}\left( x \right)} if n \geqslant k + 2.} \end{array}} \right.$$

Keywords: Variable Coefficient; Binary Sequence; Negative Binomial Distribution; Discrete Distribution; Geometric Distribution (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-1910-5_30

Ordering information: This item can be ordered from
http://www.springer.com/9789400919105

DOI: 10.1007/978-94-009-1910-5_30

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().