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x |--> x^2 + 2*x + 1
(x, k, n)
x |--> 2*x + 1
x |--> x^2 + 2*x + 1
x |--> x^2 + 2*x + 1
x |--> 4*x
x |--> (x - 1)^2 + 4*x
(x - 1)^2 - x^2 + 2*x - 1
x |--> 4*x
x |--> 4*x
0
16
81
9801
x |--> 1/(x + 1)
x |--> -1/4*x + 3/4
[1/12, 1/40, 1/144, 1/544, 1/2112, 1/8320]
x |--> 1/8*(x - 1)^2 - 1/4*x + 3/4
[1/24, 1/160, 1/1152, 1/8704, 1/67584, 1/532480]
x |--> -100*x - 80
[10000/11, 625/3, 625/14, 625/72, 625/416, 625/2688]
x |--> arctan(x)
x |--> -2*x/(x^2 + 1)^2
x |--> -3840*x^5/(x^2 + 1)^6 + 3840*x^3/(x^2 + 1)^5 - 720*x/(x^2 + 1)^4
x |--> 3715891200*x^10/(x^2 + 1)^11 - 8360755200*x^8/(x^2 + 1)^10 + 6502809600*x^6/(x^2 + 1)^9 - 2032128000*x^4/(x^2 + 1)^8 + 217728000*x^2/(x^2 + 1)^7 - 3628800/(x^2 + 1)^6
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_77.py", line 5, in <module>
taylor (h, x, _sage_const_0 , _sage_const_1 );
File "/usr/local/sage/local/lib/python2.6/site-packages/sage/calculus/functional.py", line 359, in taylor
return f.taylor(v=v,a=a,n=n)
File "expression.pyx", line 2342, in sage.symbolic.expression.Expression.taylor (sage/symbolic/expression.cpp:12460)
File "/usr/local/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1404, in __call__
return self._obj.parent().function_call(self._name, [self._obj] + list(args), kwds)
File "/usr/local/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1312, in function_call
return self.new(s)
File "/usr/local/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1096, in new
return self(code)
File "/usr/local/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1031, in __call__
return cls(self, x, name=name)
File "/usr/local/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1447, in __init__
raise TypeError, x
TypeError: Error executing code in Maxima
CODE:
sage436 : taylor(sage432,sage433,sage434,sage435)$
Maxima ERROR:
taylor: 1/2 cannot be a variable.
x |--> 1/5*x^5 - 1/3*x^3 + x
x |--> 1/9*x^9 - 1/7*x^7 + 1/5*x^5 - 1/3*x^3 + x
0.0363523909991939
0.0812500000000000
25/2
375000.000000000
-1/4*pi + 1
0.325000000000000
50
1.50000000000000e6
0.000935724332527255
0.0000141059027777778
5/2304
65.1041666666667
-1/4*pi + 13/15
0.000902777777777778
5/36
4166.66666666667
0.0000366667928446973
7.95110861842633e-12
1/817496064
0.0000366974243927369
-1/4*pi + 263/315
1.62838704505371e-8
1/399168
0.0751563251563252