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Re: Can it be done - easily?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg13241] Re: [mg13211] Can it be done - easily?
*From*: Robert Pratt <rpratt at math.unc.edu>
*Date*: Fri, 17 Jul 1998 03:17:38 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
Whether you like this or not will depend on your definition of "simple"
formula. Paste the following into a notebook to view it. Note that
the x can just be factored out of the sum.
z[x_,a_,b_,k_]:=Sum[x/y,{y,a,b,k}]
z[10000,100,1000,100]
\!\(36905\/126\)
N[%]
292.897
z[x,a,b,k]
\!\(\(x\ \((
\(-PolyGamma[0, a\/k]\) +
PolyGamma[0, 1 + a\/k + Floor[\(\(-a\) + b\)\/k]])\)\)\/k\)
?PolyGamma
"PolyGamma[z] gives the digamma function psi(z). PolyGamma[n, z] gives
the \
nth derivative of the digamma function."
Rob Pratt
Department of Mathematics
The University of North Carolina at Chapel Hill CB# 3250, 331 Phillips
Hall
Chapel Hill, NC 27599-3250
rpratt at math.unc.edu
http://www.math.unc.edu/Grads/rpratt/
On Mon, 13 Jul 1998, 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
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