“Morgan-Voyce Polynomial”的概念、定义、习题解题方法及翻译-数学辞典

单词

Morgan-Voyce Polynomial

释义

Morgan-Voyce Polynomial

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

(1)

(2)

for

, with

(3)

Alternative recurrences are

(4)

(5)

The polynomials can be given explicitly by the sums

			(6)
			(7)

Defining the Matrix

(8)

gives the identities

(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)

and

the equation

(20)

These and several other identities involving derivatives and integrals of the polynomials are given by Swamy (1968).

See also Brahmagupta Polynomial, Fibonacci Polynomial

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.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。