# Fibonacci polynomials

Fibonacci polynomials are defined recursively as follow

$${F}_{n}(x):=\{\begin{array}{cc}1\hfill & \mathrm{if}n=1;\hfill \\ x\hfill & \mathrm{if}n=2;\hfill \\ x{F}_{n-1}(x)+{F}_{n-2}(x),\hfill & \mathrm{if}n>2.\hfill \end{array}$$ |

The main (and obvious) property of this polynomials^{} is that ${F}_{n}(1)$ is ${n}^{\mathrm{th}}$ number in Fibonacci sequence^{}.

Title | Fibonacci polynomials |
---|---|

Canonical name | FibonacciPolynomials |

Date of creation | 2013-03-22 18:03:39 |

Last modified on | 2013-03-22 18:03:39 |

Owner | veselin (20506) |

Last modified by | veselin (20506) |

Numerical id | 4 |

Author | veselin (20506) |

Entry type | Definition |

Classification | msc 40-00 |