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taylor

Run Example
(%i1)taylor (sqrt (x + 1), x, 0, 5);
                              2    3      4      5
                         x   x    x    5 x    7 x
(%o1)/T/             1 + - - -- + -- - ---- + ---- + . . .
                         2   8    16   128    256
(%i2) 
Run Example
f(x):= log(x+1);
(%o1)                         f(x) := log(x + 1)
(%i2) T4(x):=taylor(f(x), x, 0, 4);
(%o2)                   T4(x) := taylor(f(x), x, 0, 4)
(%i3) T7(x):=taylor(f(x), x, 0, 7);
(%o3)                   T7(x) := taylor(f(x), x, 0, 7)
(%i4) T11(x):=taylor(f(x), x, 0, 11);
(%o4)                  T11(x) := taylor(f(x), x, 0, 11)
(%i5) T16(x):=taylor(f(x), x, 0, 16);
(%o5)                  T16(x) := taylor(f(x), x, 0, 16)
(%i6) fortran(T4(x));
      -x**4/4.0E+0+x**3/3.0E+0-x**2/2.0E+0+x
(%o6)                                done
(%i7) fortran(T7(x));
      x**7/7.0E+0-x**6/6.0E+0+x**5/5.0E+0-x**4/4.0E+0+x**3/3.0E+0-x**2/2
     1   .0E+0+x
(%o7)                                done
(%i8) fortran(T11(x));
      x**11/1.1E+1-x**10/1.0E+1+x**9/9.0E+0-x**8/8.0E+0+x**7/7.0E+0-x**6
     1   /6.0E+0+x**5/5.0E+0-x**4/4.0E+0+x**3/3.0E+0-x**2/2.0E+0+x
(%o8)                                done
(%i9) fortran(T16(x));
      -x**16/1.6E+1+x**15/1.5E+1-x**14/1.4E+1+x**13/1.3E+1-x**12/1.2E+1+
     1   x**11/1.1E+1-x**10/1.0E+1+x**9/9.0E+0-x**8/8.0E+0+x**7/7.0E+0-x
     2   **6/6.0E+0+x**5/5.0E+0-x**4/4.0E+0+x**3/3.0E+0-x**2/2.0E+0+x
(%o9)                                done
(%i10) tex(T4(x));
$$x-{{x^2}\over{2}}+{{x^3}\over{3}}-{{x^4}\over{4}}+\cdots $$
(%o10)                               false
(%i11) tex(T7(x));
$$x-{{x^2}\over{2}}+{{x^3}\over{3}}-{{x^4}\over{4}}+{{x^5}\over{5}}-
 {{x^6}\over{6}}+{{x^7}\over{7}}+\cdots $$
(%o11)                               false
(%i12) tex(T11(x));
$$x-{{x^2}\over{2}}+{{x^3}\over{3}}-{{x^4}\over{4}}+{{x^5}\over{5}}-
 {{x^6}\over{6}}+{{x^7}\over{7}}-{{x^8}\over{8}}+{{x^9}\over{9}}-{{x
 ^{10}}\over{10}}+{{x^{11}}\over{11}}+\cdots $$
(%o12)                               false
(%i13) tex(T16(x));
$$x-{{x^2}\over{2}}+{{x^3}\over{3}}-{{x^4}\over{4}}+{{x^5}\over{5}}-
 {{x^6}\over{6}}+{{x^7}\over{7}}-{{x^8}\over{8}}+{{x^9}\over{9}}-{{x
 ^{10}}\over{10}}+{{x^{11}}\over{11}}-{{x^{12}}\over{12}}+{{x^{13}
 }\over{13}}-{{x^{14}}\over{14}}+{{x^{15}}\over{15}}-{{x^{16}}\over{
 16}}+\cdots $$
(%o13)                               false
(%i14) plot2d ([f(x),T4(x),T7(x),T11(x),T16(x)],[x, -1.5, 1.5],[y, -4, 2],[legend, "log(1+x)", "y=T4", "y=T7", "y=T11", "y=T16"],[gnuplot_preamble,"set key left"]);
plotplot2d ([f(x),T4(x),T7(x),T11(x),T16(x)],[x, -1.5, 1.5],[y, -4, 2],[legend, "log(1+x)", "y=T4", "y=T7", "y=T11", "y=T16"],[gnuplot_preamble,"set key left"]);
Run Example
f(x) := %e^(-x*x);
                                         (- x) x
(%o1)                          f(x) := %e
(%i2) g(x) := taylor(f(x), x, 8, 12);
(%o2)                   g(x) := taylor(f(x), x, 8, 12)
(%i3) 

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