Re: Newbie Limit problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg53475] Re: [mg53439] Newbie Limit problem*From*: Ken Tozier <kentozier at comcast.net>*Date*: Thu, 13 Jan 2005 03:12:27 -0500 (EST)*References*: <200501120841.DAA09647@smc.vnet.net> <84C0329D-64EC-11D9-BAD8-000A95B4967A@mimuw.edu.pl>*Sender*: owner-wri-mathgroup at wolfram.com

On Jan 12, 2005, at 5:51 PM, Andrzej Kozlowski wrote: > On 12 Jan 2005, at 09:41, Ken Tozier wrote: > >> <snip> > > You are indeed doing a few things wrong but they are not responsible > for the lack of result. The first very bad thing you are doing is > writing 0.5 for the power exponent 1/2. In Mathematica these two > things > > (0.5 and 1/2) are quite different and using the former in > non-numerical > > problems can cause all sorts of weird problems. OK. didn't know that > <snip> > > But actually, the main points seem to be: > > 1) Mathematica just can't do this for general d > > 2) While it is easy to prove that the sum is convergent (see below) > do you have any special reason to expect that there is an explicit > "closed" formula for it? I'm self taught so I wasn't aware of the official name of the class of curves I'm looking at, but have since found that they are called "trochoids" and they have a whole section devoted to them here: http://mathworld.wolfram.com/Trochoid.html. Integrals might as well be written in Martian for all the meaning I get out of them. I find them impenetrable, so I don't know if the trochoids arc length formula here: http://mathworld.wolfram.com/CurtateCycloid.html is considered "closed form" or not. > Such closed formulas are actually quite rare > so unless you are lucky neither Mathematica nor anyone else will > find > one. > > <snip> Thanks for the help Andrzej. I can see that I need to buckle down and learn some more advanced math for this one. Integrals (as specified in the above mathworld page) are incomprehensible to me. I never took calculus and since the solution involves elliptic integrals, I may have bitten off more than I can chew. Andrew Wiles used elliptic curves to prove FLT so elliptics must be REALLY advanced stuff. Thanks again Ken > > > > Andrzej Kozlowski > Chiba, Japan > http://www.akikoz.net/~andrzej/ > http://www.mimuw.edu.pl/~akoz/ >

**References**:**Newbie Limit problem***From:*Ken Tozier <kentozier@comcast.net>