Re: fractional derivative (order t) of (Log[x])^n and Log[Log[x]] etc.?

*To*: mathgroup at smc.vnet.net*Subject*: [mg91284] Re: [mg91265] fractional derivative (order t) of (Log[x])^n and Log[Log[x]] etc.?*From*: Curtis Osterhoudt <cfo at lanl.gov>*Date*: Wed, 13 Aug 2008 04:41:01 -0400 (EDT)*Organization*: LANL*References*: <200808120847.EAA18835@smc.vnet.net>*Reply-to*: cfo at lanl.gov

Hi, Michael, If you go to the link you mention, and then click on the formula you're interested in, you should be taken to a page which contains the InputForm of that formula. For example, I clicked on the 6th one down, which takes me to http://functions.wolfram.com/ElementaryFunctions/Log/20/03/0006/. This page contains the InputForm of that formula, which I can then paste into Mathematica: D[Log[z]^n, {z, \[Alpha]}] == FDLogConstant[z, 0, n, \[Alpha]]/z^\[Alpha] /; Element[n, Integers] && n > 0 . Hope that helps! C.O. On Tuesday 12 August 2008 02:47:10 hanrahan398 at yahoo.co.uk wrote: > I'd be grateful if someone could tell me a nicely computable formula > for the fractional derivative w.r.t. x (order t) of (Log[x])^n, where > n is a positive integer. > > (Ideally I would like a formula where t can be any real number, but > one for t>=0 would be most helpful!) > > The second thing I am seeking is a formula for the fractional > derivative w.r.t. x (order t) of Log[Log[x]], Log[Log[Log[x]]], etc., > and more generally, of Log[...[Log[Log[x]]...], where there are n > nested log functions, where n is of course a positive integer. > > (I have visited: > <http://functions.wolfram.com/ElementaryFunctions/Log/20/03/>, and > there is a formula there for the t-th (fractional) derivative of > Log[x]^n, but I do not understand how to input it!! > > Basically I need formulae for the order-t fractional derivatives of > (Log[x])^n and of Log[Log[x]], Log[Log[Log[x]]] (and generally with n > nested logs), which I can use for variable x and given values of n and > t, and can also evaluate at given values of x. > > Many thanks in advance. > > Michael -- ========================================================== Curtis Osterhoudt cfo at remove_this.lanl.and_this.gov PGP Key ID: 0x4DCA2A10 Please avoid sending me Word or PowerPoint attachments See http://www.gnu.org/philosophy/no-word-attachments.html ==========================================================

**References**:**fractional derivative (order t) of (Log[x])^n and Log[Log[x]] etc.?***From:*hanrahan398@yahoo.co.uk