Uttryck polynomet   i korrekt form för utvärdering enligt  Chu Shih-Chieh (Horner ).

 

  Lösning :


  Anm :

Det finns Horners schema  med vars hjälp man tayloruttvecklar ett polynom kring en punkt t = t0

 Först måste    beräknas :
 

Det är klart att schemat beskriver beräkning enligt Horner av  P(t=2) = 40 .

Men man kan visa att   .

 Upprepad räkning ger taylorpolynomet
 

Resultat :

 

 Härav får man också  

 Chu Shih-Chieh Born: about 1270 in China Died: about 1330

 Chu Shih-Chieh wrote two important texts in 1299 and 1303.

The first Introduction to Mathematical Studies was intended for beginners.

The second book marks the peak of Chinese mathematics and it was a long time before further  progress was made in China.
 

 The book contains a transformation method for solving equations (used up to degree 14) rediscovered  progress was made in China.

It  also contains Pascal's triangle (discovered in China earlier) and gives formulas for

  1+2+3+4+..., 1+3+6+10+..., 1+4+10+20..., 1+5+15+35+..., 1+6+21+56+... .