mersenneforum.org > Math Fractional Calculus
 Register FAQ Search Today's Posts Mark Forums Read

 2008-01-11, 06:31 #1 nibble4bits     Nov 2005 2·7·13 Posts Fractional Calculus f(x,0)=x^a f(x,1)=ax^(a-1) f(x,2)=a(a-1)x^(a-2) f(x,n)=a(a-1)(a-2)...(a-n)x^(a-n) This is of course the n'th derivative function for x^a. Now do you see why I wanted the previous two problems solved? ;) It should be very clear if you read the previous two topics that I want not only solutions for non-negative integer values of 'n' but also for non-negative real values. The idea is to extend my calculus tools' abilities. Note 1: Not all f(x) with f'(x) has more than the whole number solutions? I'll have to do more research before I can say that definitively! Note 2: I originally called this 'recursive derivatives' because of the frist paragraph but found references to 'fractional calculus' at Wikipedia. This matches the overall post.
 2008-01-11, 08:53 #2 Orgasmic Troll Cranksta Rap Ayatollah     Jul 2003 641 Posts http://en.wikipedia.org/wiki/Differintegral specifically, I think this is what you want (where $\alpha$ is your n) Attached Thumbnails   Last fiddled with by Orgasmic Troll on 2008-01-11 at 08:55
 2008-01-11, 21:46 #3 nibble4bits     Nov 2005 2·7·13 Posts Holy calculators Batman - someone actually replied! ;) Yeah, that's another good article on Wikipedia for this subject. 'Fractional calculus' is kind of a misnomer since real values are allowed as well. I was working from the derivative point of view, but according to those articles the derivatives are sometimes actually worse than integrals.

 Similar Threads Thread Thread Starter Forum Replies Last Post Unregistered Homework Help 1 2012-02-09 04:35 davieddy Puzzles 0 2011-02-07 09:41 Primeinator Analysis & Analytic Number Theory 15 2011-01-12 23:05 davieddy Puzzles 6 2007-09-18 10:00 JustinJS Homework Help 4 2005-09-16 12:36

All times are UTC. The time now is 06:29.

Fri Aug 14 06:29:42 UTC 2020 up 1 day, 3:05, 1 user, load averages: 1.84, 1.37, 1.34