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Astro*Dictionary by Michael Erlewine





1 article for "Binomial Theorem"

Binomial Theorem [Astro*Index]

Used extensively in manipulating the equations that arise in celestial mechanics. A theorem for the expansion of a power of a binomial.

The first term in the expansion of (x+y)n is xn; the second term is nxn-1y; the third term is n(n-1)xn- 2y2/2!; in subsequent terms, the powers of x decrease and the powers of y increase; the coefficients are known as Binomial Coefficients, and are denoted by the symbol C(n,r). Thus,

    (x+y)3 = x3 + 3x2y + 3xy2 + y3

In general,

    (x+y)n = är C(n,r) xn-ryr, r = 0,1,...n


    C(n,r) = n!/[r!(n-r)!]


Astro*Index Copyright © 1997 Michael Erlewine