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MathGroup Archive 2003

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Incorrect infinite product?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44291] Incorrect infinite product?
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Tue, 4 Nov 2003 03:24:19 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Mathematica 5.0 says that

  Product[-n, {n, 1, Infinity}]

is 0, while version 4.2 says, more reasonably IMO, that it's Indeterminate.

I'm familiar with some of the different methods of summing divergent
series (Cesaro, etc.), and I'm sure there must be similar methods -- with
which I'm not familiar -- for divergent products.

So I must ask: In saying that the product is 0, is Mathematica 5.0
correctly doing something sophisticated that I'm not familiar with, or is
it simply wrong? (I'm inclined to suppose the latter, BTW.)

David Cantrell


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