Polynomials Related to Generalized Fibonacci Sequence
The Fibonacci polynomials are a polynomial sequence that can be considered as a generalization of the Fibonacci numbers. Fibonacci polynomials are defined by a recurrence relation: Fnx=xFn−1x+Fn−2x,n≥2 where F0=0,F1=1. The first few Fibonacci polynomials are F0=0, F0x=0, F1x=1, F2x=x, F3x=x2+1. In t...
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| Autores principales: | , |
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| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
| Publicado: |
IntechOpen
2023
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| Materias: | |
| Acceso en línea: | https://www.intechopen.com/chapters/86784 |
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| Sumario: | The Fibonacci polynomials are a polynomial sequence that can be considered as a generalization of the Fibonacci numbers. Fibonacci polynomials are defined by a recurrence relation: Fnx=xFn−1x+Fn−2x,n≥2 where F0=0,F1=1. The first few Fibonacci polynomials are F0=0, F0x=0, F1x=1, F2x=x, F3x=x2+1. In this chapter, we extend the Fibonacci recurrence relation to define the sequence {Kn} and will derive some properties of this sequence. We also define four comparison sequences {Pn}, {Qn}, {Rn}, and {Sn} and obtain some identities with the help of generating matrix. |
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| ISBN: | 978-1-83768-502-8 |
| DOI: | 10.5772/intechopen.110481 |