A curious property of series involving terms of generalized sequences (Q1974409)
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: A curious property of series involving terms of generalized sequences |
scientific article; zbMATH DE number 1439628
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A curious property of series involving terms of generalized sequences |
scientific article; zbMATH DE number 1439628 |
Statements
A curious property of series involving terms of generalized sequences (English)
0 references
21 May 2002
0 references
Motivated by the fact that \(\Sigma F_n/2^n= \Sigma nF_n/2^n\), \(F_n\) being the \(n\)-th Fibonacci number, the authors look more generally for those triples \((p,q,r)\) for which the series \(\Sigma U_n(p,q)/r^n\) resp. \(\Sigma V_n(p,q)/r^n\) are indifferent towards introducing the factor \(n\) \((U_n, V_n\) denoting as usual the generalized Fibonacci resp. Lucas numbers). An application to special trigonometric series is given.
0 references
generalized Fibonacci number
0 references
generalized Lucas number
0 references
power series
0 references
