A set of identities involving 
-dimensional visible lattice points was discovered by Campbell
(1994). Examples include
 |
for 
and
![product_((a,b,c)=1; a,b>=0,c<=1)(1-x^ay^bz^c)^(-1/c)=(1-z)^(-1/[(1-x)(1-y)])](/images/equations/VisiblePointVectorIdentity/NumberedEquation2.svg) |
for 
.
Visible Point Vector Identity
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References
Campbell, G. B. "Infinite Products Over Visible Lattice Points." Internat. J. Math. Math. Sci. 17, 637-654, 1994.Campbell, G. B. "Visible Point Vector Identities." http://www.geocities.com/CapeCanaveral/Launchpad/9416/vpv.html.Referenced on Wolfram|Alpha
Visible Point Vector IdentityCite this as:
Weisstein, Eric W. "Visible Point Vector Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VisiblePointVectorIdentity.html