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pade-tan-taylor

pade (taylor(tan(x), ...

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pade-taylor

t: taylor ( (-x^2-x)/...

pade (t, 3, 3);

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pade-taylor

pade(taylor((x^(1-q)-...

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pade-taylor

pade(taylor((x^(1-q)-...

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pade-taylor

t: taylor (1 + x + x^...

pade (t, 3, 3);

Calculate

pade-taylor

pade(taylor((e^x-1)/x...

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pade-plot2d-taylor
plot2d([f(x), p(x)], [x, -6, 6]);

f(x) := e^(-x*x);

n : 64;

g(x) := taylor(f(x), ...

Calculate

pade-taylor

t: taylor(ln(x),x,1,3);

pade(t,3,3);

Calculate

pade-plot2d-taylor
plot2d([f(x), p(x)], [x, -1, 1]);

f(x) := %e^(-x*x);

n : 20;

g(x) := taylor(f(x), ...

Calculate

pade-taylor

pade(taylor((x^(1-q)-...

Calculate

pade

Run Example
(%i1)pade(taylor(sin(x),x,0,7),7,1);
                           7       5        3
                          x  - 42 x  + 840 x  - 5040 x
(%o1)                  [- ----------------------------]
                                      5040
(%i2) 
Run Example
fullratsimp (pade (taylor (exp (x), x, 0, 8), 4, 4));
                       4       3        2
                      x  + 20 x  + 180 x  + 840 x + 1680
(%o1)                [----------------------------------]
                       4       3        2
                      x  - 20 x  + 180 x  - 840 x + 1680
(%i2) 
Run Example
f(x) := x^(1/12);
                                          1/12
(%o1)                            f(x) := x
(%i2) k : 6;
(%o2)                                  6
(%i3) n : 2 * k;
(%o3)                                 12
(%i4) t(x) := taylor(f(x), x, 1/3, n);
                                                 1
(%o4)                    t(x) := taylor(f(x), x, -, n)
                                                 3
(%i5) t(x);
                       1/12 11      1          1/12 11       1 2
           1/12 11   (3    )   (x - -)   (11 (3    )  ) (x - -)
         (3    )                    3                        3
(%o5)/T/ --------- + ----------------- - -----------------------
             3              12                     96
          1/12 11       1 3           1/12 11       1 4
   (253 (3    )  ) (x - -)    (8855 (3    )  ) (x - -)
                        3                           3
 + ------------------------ - -------------------------
             1152                       18432
            1/12 11       1 5              1/12 11       1 6
   (83237 (3    )  ) (x - -)    (4910983 (3    )  ) (x - -)
                          3                              3
 + -------------------------- - ----------------------------
             73728                        1769472
               1/12 11       1 7                 1/12 11       1 8
   (49811399 (3    )  ) (x - -)    (4134346117 (3    )  ) (x - -)
                             3                                 3
 + ----------------------------- - -------------------------------
              7077888                         226492416
                   1/12 11       1 9                    1/12 11       1 10
   (392762881115 (3    )  ) (x - -)    (8405125655861 (3    )  ) (x - -)
                                 3                                    3
 + --------------------------------- - -----------------------------------
              8153726976                           65229815808
                     1/12 11       1 11
   (90928177549769 (3    )  ) (x - -)
                                   3
 + ------------------------------------
               260919263232
                        1/12 11       1 12
   (11911591259019739 (3    )  ) (x - -)
                                      3
 - --------------------------------------- + . . .
               12524124635136
(%i6) pade(t(x), n/2, n/2);
                     6                 5                  4                 3
(%o6) [(54650399895 x  + 596950521930 x  + 1174002693129 x  + 662800319244 x
                 2
 + 118357199865 x  + 5950198026 x + 49811399)
   1/12               6                5                4                3
/(3     (36312509871 x  - 72625019742 x  + 60520849785 x  - 26898155460 x
               2
 + 6724538865 x  - 896605182 x + 49811399)
    13/12                5                 4                 3
 + 3      (184863686616 x  + 334897983000 x  - 651934740240 x
                 2
 + 360201386160 x  - 83848532040 x + 7177566648)
    25/12                3                 2
 + 3      (293944743936 x  - 293944743936 x  + 97981581312 x - 10886842368)
    37/12               2
 + 3      (62541434880 x  - 23037861888 x + 2832371712))]
(%i7) p(x) := pade(t(x), n/2, n/2)[1];
                                              n  n
(%o7)                      p(x) := pade(t(x), -, -)
                                              2  2
                                                   1
(%i8) pp(x) := bfloat(p(x));
(%o8)                        pp(x) := bfloat(p(x))
(%i9) pp(x);
                               6                    5                      4
(%o9) (1.0b0 (5.4650399895b10 x  + 5.9695052193b11 x  + 1.174002693129b12 x
                     3                     2
 + 6.62800319244b11 x  + 1.18357199865b11 x  + 5.950198026b9 x + 4.9811399b7))
                                        6                    5
/(1.095872691135244b0 (3.6312509871b10 x  - 7.2625019742b10 x
                    4                   3                  2
 + 6.0520849785b10 x  - 2.689815546b10 x  + 6.724538865b9 x  - 8.96605182b8 x
                                                         5                  4
 + 4.9811399b7) + 3.287618073405733b0 (1.84863686616b11 x  + 3.34897983b11 x
                    3                    2
 - 6.5193474024b11 x  + 3.6020138616b11 x  - 8.384853204b10 x + 7.177566648b9)
                                          3                     2
 + 9.862854220217199b0 (2.93944743936b11 x  - 2.93944743936b11 x
 + 9.7981581312b10 x - 1.0886842368b10)
                                       2
 + 2.95885626606516b1 (6.254143488b10 x  - 2.3037861888b10 x + 2.832371712b9))
(%i10) l : 2^-12;
                                      1
(%o10)                               ----
                                     4096
(%i11) r : 2^0;
(%o11)                                 1
(%i12) plot2d([(f(x)-pp(x))/f(x)], [x, l, r]);
plotplot2d([(f(x)-pp(x))/f(x)], [x, l, r]);

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Help for Pade