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Product of a sequence identities

by eddybob123
Tags: identities, product, sequence
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eddybob123
#1
Apr7-13, 03:04 PM
P: 115
HI, does anyone know a decent site where I can find a few product identities? I googled it, but all that came up were trig identities. I am not looking for those; I am specifically looking for product of a sequence identities: ∏
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henpen
#2
Apr8-13, 04:26 PM
P: 50
http://en.wikipedia.org/wiki/Wallis_product
http://en.wikipedia.org/wiki/List_of...volving_%CF%80

I doubt whether you've not looked at this already, but posting just in case it's of use.
eddybob123
#3
Apr8-13, 06:30 PM
P: 115
Those are quite interesting, but not what I am looking for. I mean if there are any sites that post a full list of identities, not just specific ones. That would be very helpful.

Stephen Tashi
#4
Apr8-13, 06:56 PM
Sci Advisor
P: 3,314
Product of a sequence identities

Quote Quote by eddybob123 View Post
Those are quite interesting, but not what I am looking for. I mean if there are any sites that post a full list of identities, not just specific ones. That would be very helpful.
It's an interesting question what would constitute a "non-trivial" product identity. An additive identity [itex] \sum_{i=1}^{\infty} X_i = Y [/itex] implies a product identity [itex] \prod_{i=1}^{\infty} e^{x_i} = e^Y [/itex]. A product identity that had negative factors could not be converted back into an additive identity by taking logarithms, but there might be some other methods of transformation that would revert it to an additive identity.
eddybob123
#5
Apr8-13, 09:36 PM
P: 115
Never mind I found this great one:
http://pi.physik.uni-bonn.de/~dieckm...d/InfProd.html


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