Taylor Coefficient

u t. 0 0 0

u t. y is yth coefficient 在Taylor series approximation to 函數 u . domain of 副詞 t. is same as 左 domain of導函數 D. .See case m t. . x u t.y is product of (x^y) and u t. y .

例如:

   f=: 1 2 1&p. [. g=: 1 3 3 1&p. [. x=: 10%~i=: i.8
   ]c=: (f*g) t. i
1 5 10 10 5 1 0 0

   6.2 ":(c p. x),:(f*g) x
  1.00  1.61  2.49  3.71  5.38  7.59 10.49 14.20
  1.00  1.61  2.49  3.71  5.38  7.59 10.49 14.20

   (c p. x)=(f*g) x
1 1 1 1 1 1 1 1
            
   ]d=: f@g t. i 
4 12 21 22 15 6 1 0

   (d p. x)=(f g x)
1 1 1 1 1 1 1 1

   sin=: 1&o. [. cos=: 2&o.
   8.4":t=: (^ t. i),(sin t. i),:(cos t. i)
  1.0000  1.0000  0.5000  0.1667  0.0417  0.0083  0.0014  0.0002
  0.0000  1.0000  0.0000 _0.1667  0.0000  0.0083  0.0000 _0.0002
  1.0000  0.0000 _0.5000  0.0000  0.0417  0.0000 _0.0014  0.0000

   * t
1 1  1  1 1 1  1  1
0 1  0 _1 0 1  0 _1
1 0 _1  0 1 0 _1  0

   ((sin*sin)+(cos*cos)) t. i
1 0 0 0 _2.71051e_20 0 0 0

   rf=: n%d [. n=: 0 1&p. [. d=: 1 _1 _1&p.
   ]fibonacci=: rf t. i. 20
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181

   2 +/\ fibonacci
1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

   (% -. - *:) t. i.20
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181

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