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MathGroup Archive 1998

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Re: Can it be done - easily?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13298] Re: Can it be done - easily?
  • From: Tobias Oed <tobias at physics.odu.edu>
  • Date: Fri, 17 Jul 1998 03:18:49 -0400
  • Organization: Old Dominion University
  • References: <6od25q$hn9@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Barry Culhane wrote:
> 
> Myself and two workmates are software developers.  One guy wanted a
> formula to calculate a result for the following equation...
>      Z = sum of X/Y where X is a fixed number, and Y ranges from A-B in
> fixed steps...
>      i.e... X=10000 ; Y=100,200,300...1000
>      i.e... Z= 10000/100 + 10000/200 + ... 10000/1000 =  292.896
> 
> He and I tried to figure out a simple formula to calculate it, but
> couldn't. The third guy said it was *not* *possible* to derive a
> formula - we think he's wrong, but can't prove it.  MathCad can solve
> it in the blink of an eye, even if the value of Y ranges from 1 to 1e6
> in steps of 1 !!!
> 
> Can anyone come up with a simple formula to give a reasonably accurate
> result?  It is too slow to actually divide X by Y for each value of Y
> as there may be 1000 or even 100,000 values of Y.
> 
> Thanks in advance...
> > Barry Culhane
> > Schaffner Ltd, Limerick, IRELAND

This is what mathematica says:

***** In[214]:= 
Sum[X/i,{i,A,B,C}] //InputForm

Out[214]//InputForm= (X*(-PolyGamma[0, A/C] + PolyGamma[0, 1 + A/C +
Floor[(-A + B)/C]]))/C

I don't know what polygamma that's the online help:

***** In[215]:= 
??PolyGamma
PolyGamma[z] gives the digamma function psi(z). PolyGamma[n, z] gives
the nth derivative of the digamma
   function.

Attributes[PolyGamma] = {Listable, NHoldFirst, Protected}

hope you can do something with this
Tobias


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