Number theory and special functions (Q2751688)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Number theory and special functions |
scientific article; zbMATH DE number 1665033
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Number theory and special functions |
scientific article; zbMATH DE number 1665033 |
Statements
8 July 2003
0 references
Catalan numbers
0 references
polynomials
0 references
recurrence relations
0 references
summation formulae
0 references
Number theory and special functions (English)
0 references
Two \(q\)-analogues of the numbers NEWLINE\[NEWLINE f(n,k) = (-1)^{n-k}{2n+1 \choose n-k}L_{2k+1},\qquad 0\leq k\leq n, NEWLINE\]NEWLINE where \(L_k\) is the \(k\)th Lucas number, are studied. These \(q\)-analogues are polynomials in \(q\). A table containing the first few polynomials is provided, and the degree is computed for general \(k\) and \(n\). Some recurrence relations and other properties, including a combinatorial interpretation in terms of partitions, are given.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00018].
0 references
