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taytorat

Run Example
(%i1)taylor2(fn,x,y,point,N):=taytorat(taylor(taylor(fn,x,point,N),y,point,N));
(%o1) taylor2(fn, x, y, point, N) := taytorat(taylor(taylor(fn, x, point, N), 
                                                                  y, point, N))
(%i2) taylor2(sin(x+y),x,y,0,5);
            4       2        5     5       3           4
(%o2)/R/ ((x  - 12 x  + 24) y  + (x  - 20 x  + 120 x) y
          4        2         3          5        3            2
 + (- 20 x  + 240 x  - 480) y  + (- 12 x  + 240 x  - 1440 x) y
         4         2                 5        3
 + (120 x  - 1440 x  + 2880) y + 24 x  - 480 x  + 2880 x)/2880
(%i3) 
Run Example
/* Zu entwickelndes Polynom */p:x^3-3*x^2+5*x-1;
                               3      2
(%o1)                         x  - 3 x  + 5 x - 1
(%i2) n:hipow(p,x);
(%o2)                                  3
(%i3) t:taylor(p,x,a,n);
                        2    3       2                                       2
(%o3)/T/ - 1 + 5 a - 3 a  + a  + (3 a  - 6 a + 5) (x - a) + (3 a - 3) (x - a)
                                                                      3
                                                             + (x - a)  + . . .
(%i4) taytorat(t);
                3                    2       2                       3      2
(%o4)/R/ (x - a)  + (3 a - 3) (x - a)  + (3 a  - 6 a + 5) (x - a) + a  - 3 a
                                                                      + 5 a - 1
(%i5) 
Run Example
p:x^3-3*x^2+5*x-1;
                               3      2
(%o1)                         x  - 3 x  + 5 x - 1
(%i2) n:hipow(p,x);
(%o2)                                  3
(%i3) t:taylor(p,x,a,n);
                        2    3       2                                       2
(%o3)/T/ - 1 + 5 a - 3 a  + a  + (3 a  - 6 a + 5) (x - a) + (3 a - 3) (x - a)
                                                                      3
                                                             + (x - a)  + . . .
(%i4) taytorat(t);
                3                    2       2                       3      2
(%o4)/R/ (x - a)  + (3 a - 3) (x - a)  + (3 a  - 6 a + 5) (x - a) + a  - 3 a
                                                                      + 5 a - 1
(%i5) 

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