Article
| Title: | On one-parameter generalization of Fibonacci and Leonardo elliptic quaternions (English) |
| Author: | Bród, Dorota |
| Author: | Szynal-Liana, Anetta |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 71 |
| Issue: | 3 |
| Year: | 2026 |
| Pages: | 353-364 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The motion of a point on an ellipsoid can be interpreted using the generation of elliptical rotations. An elliptical rotation can be defined using elliptic quaternions. The Fibonacci sequence, defined by the second-order linear relation, is a famous sequence used in mathematics, physics, computer science, technical analysis and others. In this paper, we introduce and study generalized Fibonacci-Leonardo elliptic quaternions, which generalize the Fibonacci elliptic quaternions and Leonardo elliptic quaternions, simultaneously. We give the ordinary generating functions, the Binet-type formulas, general bilinear index-reduction formulas, and the sum of the finite, finite odd, and finite even terms of these quaternions. (English) |
| Keyword: | quaternion |
| Keyword: | elliptic quaternion |
| Keyword: | Fibonacci number |
| Keyword: | Leonardo number |
| MSC: | 11B37 |
| MSC: | 11B39 |
| DOI: | 10.21136/AM.2026.0120-26 |
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| Date available: | 2026-07-02T06:51:43Z |
| Last updated: | 2026-08-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153672 |
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