Polynomials related to the Brahmagupta Polynomials. They are defined by the
Recurrence Relations

(1) |

(2) |

(3) |

(4) |

(5) |

(6) | |||

(7) |

Defining the Matrix

(8) |

(9) |

(10) |

Defining

(11) | |||

(12) |

gives

(13) | |||

(14) |

and

(15) | |||

(16) |

The Morgan-Voyce polynomials are related to the Fibonacci Polynomials by

(17) | |||

(18) |

(Swamy 1968).

satisfies the Ordinary Differential Equation

(19) |

(20) |

**References**

Lahr, J. ``Fibonacci and Lucas Numbers and the Morgan-Voyce Polynomials in Ladder Networks and in Electric Line
Theory.'' In *Fibonacci Numbers and Their Applications* (Ed. G. E. Bergum, A. N. Philippou, and A. F. Horadam).
Dordrecht, Netherlands: Reidel, 1986.

Morgan-Voyce, A. M. ``Ladder Network Analysis Using Fibonacci Numbers.'' *IRE Trans. Circuit Th.* **CT-6**, 321-322, Sep. 1959.

Swamy, M. N. S. ``Properties of the Polynomials Defined by Morgan-Voyce.'' *Fib. Quart.* **4**, 73-81, 1966.

Swamy, M. N. S. ``More Fibonacci Identities.'' *Fib. Quart.* **4**, 369-372, 1966.

Swamy, M. N. S. ``Further Properties of Morgan-Voyce Polynomials.'' *Fib. Quart.* **6**, 167-175, 1968.

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1999-05-26