Brahmagupta Polynomial

One of the polynomials obtained by taking powers of the Brahmagupta matrix. They satisfy the recurrence relation

			(1)
			(2)

A list of many others is given by Suryanarayan (1996). Explicitly,

			(3)
			(4)

The Brahmagupta polynomials satisfy

			(5)
			(6)

The first few polynomials are

			(7)
			(8)
			(9)
			(10)
			(11)

and

			(12)
			(13)
			(14)
			(15)
			(16)

Taking  and  gives  equal to the Pell numbers and  equal to half the Pell-Lucas numbers. The Brahmagupta polynomials are related to the Morgan-Voyce polynomials, but the relationship given by Suryanarayan (1996) is incorrect.

REFERENCES:

Suryanarayan, E. R. "The Brahmagupta Polynomials." Fib. Quart. 34, 30-39, 1996.