Visible Point Vector Identity

A set of identities involving n-dimensional visible lattice points was discovered by Campbell (1994). Examples include

[画像: product_((a,b)=1; a>=0,b<=1)(1-y^az^b)^(-1/b)=(1-z)^(-1/(1-y)) ]

for |yz|,|z|<1 and

[画像: product_((a,b,c)=1; a,b>=0,c<=1)(1-x^ay^bz^c)^(-1/c)=(1-z)^(-1/[(1-x)(1-y)]) ]

for |xyz|,|xz|,|yz|,|z|<1.

Explore with Wolfram|Alpha

WolframAlpha

More things to try:

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 Identity

Cite this as:

Weisstein, Eric W. "Visible Point Vector Identity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VisiblePointVectorIdentity.html

Subject classifications