Re: New Analytical Functions - Mathematica Verified

*To*: mathgroup at smc.vnet.net*Subject*: [mg66916] Re: New Analytical Functions - Mathematica Verified*From*: "Mohamed Al-Dabbagh" <mohamed_al_dabbagh at hotmail.com>*Date*: Sat, 3 Jun 2006 03:26:29 -0400 (EDT)*Organization*: http://groups.google.com*References*: <200605280104.VAA23436@smc.vnet.net> <200606011055.GAA20733@smc.vnet.net> <e5osg1$hvp$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Daniel Lichtblau wrote: > They will change the behavior of its derivatives. Actually I think I did > not want to use the DiracDelta component in that particular definition > (or else to use further derivatives thereof in the definition for higher > derivatives of FractionalPart). > ........................... > ........................... > Did you try it? > Dan, Your usage of DiracDelta has made some remarkable correction for the result, but on a very high cost of runtime! I have made some experiments and wanted to publish them. You should remember that my paper: http://dabbagh2.fortunecity.com/disc has proved that the derivative of the fractional part of any function is the SAME as derivative of that function WITHOUT involving in the calculation of fractional part! When I used your improvement using Dirac Delta, a very substantial improvement occurred on the numerical results. HOWEVER, this lead to some very long delays. To the extent that calculating 5th derivative of the FractionalPart(x^5) to 1000 places of decimal would take about ONE HOUR!!!! Here are some results I arranged it in a page prepared for you: http://dabbagh2.fortunecity.com/lichtblau/ You will see how my formulas are A LOT faster. Mohamed Al-Dabbagh

**Follow-Ups**:**Re: Re: New Analytical Functions - Mathematica Verified***From:*Daniel Lichtblau <danl@wolfram.com>

**References**:**Re: New Analytical Functions - Mathematica Verified***From:*"Mohamed Al-Dabbagh" <mohamed_al_dabbagh@hotmail.com>