Spreadsheet in Maple

1 Use the spreadsheet in Maple to experiment with the 3x + 1 problem.
2 How is the number pattern related to the sucessive derivatives of tan(x) formed?
3 How is the number pattern related to the sucessive derivatives of cot(x) formed?
4 Express tan(nx) as a rational function of tan(x) for n = 1,2,3,4,5,6.
5 Study the number pattern associated with the indefinite integral of the function xnex.
6 List the Chebyshev polynomials Tn(x) for n = 0,1,2,3,4,5,6.

1 Use the spreadsheet in Maple to experiment with the 3x + 1 problem.

> f:=x->if x mod 2=0 then x/2 else 3*x+1 fi;

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2 How is the number pattern related to the sucessive derivatives of tan(x) formed?

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3 How is the number pattern related to the sucessive derivatives of cot(x) formed?

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4 Express tan(nx) as a rational function of tan(x) for n = 1,2,3,4,5,6.

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5 Study the number pattern associated with the indefinite integral of the function xnex.

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6 List the Chebyshev polynomials Tn(x) for n = 0,1,2,3,4,5,6.

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Factoring

1 Find an exponent n such that some coefficients appearing in the factorization of xn - 1 are different from 0, -1 and
1.
Reference: 吳振奎，數學中的美--數學美學初探，天津教育，(1996), p. 143.

> factor(x^99-1);

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Factor (((x2 - a)2 - a)2 - a)2 - a - x.
Reference: Ramanujan's Notebooks IV, p. 42.

> restart:

> factor((x^2-a)^2-a-x);

> factor((((x^2-a)^2-a)^2-a)^2-a-x);

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