14 lines
572 B
Text
14 lines
572 B
Text
deftaylor(f(x), sum(n! * x^n, n, 0, inf))$
|
|
|
|
taylor(f(x), x, 0, 10);
|
|
/ * 1 + x + 2 * x^2 + 6 * x^3 + 24 * x^4 + 120 * x^5 + 720 * x^6 + 5040 * x^7 + 40320 * x^8 + 362880 * x^9 + 3628800 * x^10 + ... * /
|
|
|
|
taylor(f(x)^2, x, 0, 10);
|
|
/ * 1 + 2 * x + 5 * x^2 + 16 * x^3 + 64 * x^4 + 312 * x^5 + 1812 * x^6 + 12288 * x^7 + 95616 * x^8 + 840960 * x^9 + 8254080 * x^10 + ... * /
|
|
|
|
|
|
deftaylor(fcos(x), sum((-1)^n * x^(2 * n) / (2 * n)!, n, 0, inf))$
|
|
deftaylor(fsin(x), sum((-1)^n * x^(2 * n + 1) / (2 * n + 1)!, n, 0, inf))$
|
|
|
|
taylor(fcos(x)^2 + fsin(x)^2, x, 0, 20);
|
|
/ * 1 + ... * /
|