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Consider the generating functions

A=1+x+x2,B=1+2x+4x4+x5,C=1x2+x4,D=1+x+x2+x3+,E=1+x3+x6+x9+,F=1x+x2x3+x4.\begin{array}{ll} A=1+x+x^2, & B=1+2 x+4 x^4+x^5, \\ C=1-x^2+x^4, & D=1+x+x^2+x^3+\cdots, \\ E=1+x^3+x^6+x^9+\cdots, & F=1-x+x^2-x^3+x^4-\cdots . \end{array}

In exercise given below, write each indicated expression in the form

a0+a1x+a2x2+a3x3+.a_0+a_1 x+a_2 x^2+a_3 x^3+\cdots .

If the expression is a polynomial, then compute it completely; otherwise compute it through the x7x^7 term.



Answered 1 year ago
Answered 1 year ago
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We have to calculate the product of two expressions, AA, and DD:

A=1+x+x2D=1+x+x2+.\begin{align*} A&=1+x+x^2\\ D&=1+x+x^2+\cdots. \end{align*}

AA is a polynomial and DD is a generating function. We only have to calculate the first 88 terms because DD isn't a polynomial.

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