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MathGroup Archive 2006

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Re: Problem with derivate of product

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67322] Re: Problem with derivate of product
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sun, 18 Jun 2006 05:13:15 -0400 (EDT)
  • References: <e70fid$rmp$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Esa A E Peuha schrieb:
> Mathematica 5.0 seems to have trouble with parsing this input:
> 
> In[1]:= D[Product[f[k,z],{k,0,m}],{z,n}]
> 
> Out[1]= D[Product[f[k, z], {k, 0, m}], z]
> 
> Has this been fixed in newer versions?
> 
Hi Esa,

I don't know what's going on there, but

pfn = Derivative[n][Product[f[k, #1], {k, 0, m}] & ][z]
   Derivative[n][Product[f[k, #1], {k, 0, m}] & ][z]

seems to be a workaround:

Expand[pfn /. {f -> (1 + #2/(1 + #1) & ), m -> 5, n -> 2}]
   203/45 + (49*z)/8 + (35*z^2)/12 + (7*z^3)/12 + z^4/24

Expand[D[Times @@ (1 + z/(1 + #1) & ) /@ Range[0, 5], {z, 2}]]
   203/45 + (49*z)/8 + (35*z^2)/12 + (7*z^3)/12 + z^4/24

Peter


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