Product of a sequence identities


by eddybob123
Tags: identities, product, sequence
eddybob123
eddybob123 is offline
#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
henpen is offline
#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
eddybob123 is offline
#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
Stephen Tashi is offline
#4
Apr8-13, 06:56 PM
Sci Advisor
P: 3,167

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
eddybob123 is offline
#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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