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Re: Re: Re: extracting fractional powers of series expansion?

• To: mathgroup at smc.vnet.net
• Subject: [mg78383] Re: [mg78324] Re: [mg78257] Re: extracting fractional powers of series expansion?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 29 Jun 2007 05:54:53 -0400 (EDT)
• References: <26396889.1182938859211.JavaMail.root@m35> <200706280828.EAA20651@smc.vnet.net>

I don't think the concept of "coefficient" is well defined except in  
the case of a power series (including fractional power series like  
Puiseux series) and Series[x!, {x, Infinity, m} (m any positive  
integer) is not a power series but an "asymptotic expansion" (in  
fact, essentially the same as the second one on this page

http://functions.wolfram.com/GammaBetaErf/Gamma/06/02/ ).

As Dimitris recently pointed out, Mathematica will sometimes return  
such asymptotic expansions and sometimes won't and it is not clear  
(to me) exactly when it wil do so (and why).


Andrzej Kozlowski


On 28 Jun 2007, at 17:28, DrMajorBob wrote:

> Just that it doesn't always work:
>
> SeriesCoefficient[x!, {x, Infinity, 5/2}]
>
> SeriesCoefficient[x!, {x, \[Infinity], 5/2}]
>
> Bobby
>
> On Wed, 27 Jun 2007 04:22:32 -0500, chuck009 <dmilioto at comcast.com>  
> wrote:
>
>> What's wrong with just using the negative power in SeriesCoefficient:
>>
>> sval = Series[1/(x*(x^2*(1 - x^3))^(1/3)), {x, 0, 10}]
>>
>> SeriesCoefficient[sval, -5/3]
>>
>>
>
>
>
> -- 
>
> DrMajorBob at bigfoot.com
>

• References:
  • Re: Re: extracting fractional powers of series expansion?
    • From: DrMajorBob <drmajorbob@bigfoot.com>