Function: taylor (expr, x, a, n)
Function: taylor (expr, [x_1, x_2, ...], a, n)
Function: taylor (expr, [x, a, n, 'asymp])
Function: taylor (expr, [x_1, x_2, ...], [a_1, a_2, ...], [n_1, n_2, ...])
Function: taylor (expr, [x_1, a_1, n_1], [x_2, a_2, n_2], ...)
- Expands of the expression expr in a truncated Taylor or Laurent series in the variable x around the point a, containing terms through (x - a)^n.
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Trigonometric Expansion
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(%i) taylor(sin(x), x, 0, 7);
(%o) x-x^3/6+x^5/120-x^7/5040
(%i) taylor(cos(x), x, 0, 7);
(%o) 1-x^2/2+x^4/24-x^6/720
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(%i) taylor(exp(x), x, 0, 7 );
(%o) 1+x+x^2/2+x^3/6+x^4/24+x^5/120+x^6/720+x^7/5040
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(%i) taylor(1/(1-x), x, 0, 7 );
(%o) 1+x+x^2+x^3+x^4+x^5+x^6+x^7
(%i) taylor(1/(1+x), x, 0, 7 );
(%o) 1-x+x^2-x^3+x^4-x^5+x^6-x^7
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(%i) taylor(log(1-x),x,0,7);
(%o) -x-x^2/2-x^3/3-x^4/4-x^5/5-x^6/6-x^7/7
