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Re: Re: Summation question

• To: mathgroup at smc.vnet.net
• Subject: [mg85762] Re: [mg85743] Re: [mg85664] Summation question
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 21 Feb 2008 18:01:28 -0500 (EST)
• References: <200802190647.BAA27190@smc.vnet.net> <200802201206.HAA29899@smc.vnet.net>

On 20 Feb 2008, at 13:06, Sseziwa Mukasa wrote:

>
> On Feb 19, 2008, at 1:47 AM, Robert Pigeon wrote:
>
>> Good day all,
>>
>>            I want to make a summation like this:  Sum[f[i],{i, start,
>> finish}]. What I want is that the sum be over a specific set like
>> {1,3,5,7,11,13}. So the sum would be : f[1]+f[3]+f[5]+f[7]+f[11]+f
>> [13]. The
>> set I want to use is the primes. So, how do I use, if possible, Sum
>> over a
>> specific set ?
>
> One way is to map the sum indices to the set elements eg:
>
> Sum[f[Prime[i]],{i,start,finish}]
>
> but this may present problems if the sum is over an infinite range.
>
> Regards,
>
> Sseziwa
>


In fact, Mathematica sometimes, understands infinte sums or products  
over the set of all primes, described in precisely this way. A famous  
example is:

In[6]:= Product[1 - Prime[n]^(-z), {n, 1, Infinity}]
Out[6]= 1/Zeta[z]

Andrzej Kozlowski

• References:
  • Summation question
    • From: Robert Pigeon <robert.pigeon@videotron.ca>
  • Re: Summation question
    • From: Sseziwa Mukasa <mukasa@jeol.com>