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Re: Newbie Limit problem

  • To: mathgroup at
  • Subject: [mg53475] Re: [mg53439] Newbie Limit problem
  • From: Ken Tozier <kentozier at>
  • Date: Thu, 13 Jan 2005 03:12:27 -0500 (EST)
  • References: <> <>
  • Sender: owner-wri-mathgroup at

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: 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: 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


> Andrzej Kozlowski
> Chiba, Japan

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