Re: general form of a n-derivative
- To: mathgroup at smc.vnet.net
- Subject: [mg71566] Re: [mg71542] general form of a n-derivative
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 23 Nov 2006 05:41:37 -0500 (EST)
- References: <200611221022.FAA04538@smc.vnet.net> <FB3C4201-33DA-4157-B95F-13263EA744C0@mimuw.edu.pl> <6CEACE48-9306-43DC-BD56-55D6188E61C8@mimuw.edu.pl>
There was some confusion involving indexes and powers in my earlier
posts on this topic so I have decided to restate the result again. Let
f[x_] := Exp[-(1 - x^2)^(-1)]
Then
D[f[x],{x,n}] has the form
(-1)^n*(E^(-1/(1 - x^2))/(x^2 - 1)^(2*n))*p[n][x]
where p[n][x] is a polynomial in x of the form p[n][x]= (n+1)! x^
(3n-2) + lower degree terms.
The proof, by induction, is in my two other posts in this thread,
(after correcting the statement which had the degree of p[x] as 3n+1).
Andrzej Kozlowski
Tokyo, Japan
- References:
- general form of a n-derivative
- From: Wiso <giurrerotipiacerebbe@hotmailtipiacerebbe.itipiacerebbe>
- general form of a n-derivative