Recent changes to 531: Combining Taylor series of different ordershttps://sourceforge.net/p/maxima/bugs/531/2004-03-04T19:06:19ZCombining Taylor series of different orders2004-03-04T19:06:19Z2004-03-04T19:06:19ZStavros Macrakishttps://sourceforge.net/u/macrakis/https://sourceforge.net39f2ec537341b72bb9ff344a71f8c149ba3c8d94taylor\(exp\(x\),x,0,2\) - taylor\(exp\(x\),x,0,0\)
=> x + x^2/2 + ...
This is wrong. The result should be 0+... \(order 0\).
taylor\(exp\(x\),x,0,2\) - taylor\(exp\(x\),x,0,1\)
=> 0 + ...
taylor\(exp\(x\),x,0,2\) \* taylor\(exp\(x\),x,0,5\)
=> 1 + 2\*x + 2\*x^2 + ...
This time, the printed results are correct: the
expansion is only as good as the longest of the
component expansions.
But taylorinfo of the result is \[\[x,0,2\]\], that is,
taylor thinks that it is 0 + 0\*x + 0\*x^2 + ...
taylor\(taylor\(exp\(x\),x,0,2\),x,0,5\)
=> 1 + x + x^2/2 + ...
This is correct, and the taylorinfo is correctly
\[\[x,0,2\]\], but shouldn't it give a warning?
taylor\(x^2,x,0,1\)/x politely gives a warning \("0+...
assumed to be zero in Taylor"\), but the result has
taylorinfo \[\[x,0,2\]\]. Shouldn't it have taylorinfo
\[\[x,0,1\]\]?
-s