Visible point vector summations from hypercube and hyperpyramid lattices
New identities are given, based on ideas related to visible (from the origin) point vectors. Each result was found from summing on vpv lattices dividing space into radial regions from the origin. This is related to recent work by the author in which new partition type infinite products were deriv...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298001033 |
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| Summary: | New identities are given, based on ideas related to visible (from the origin) point vectors. Each result was found from summing on vpv lattices dividing space
into radial regions from the origin. This is
related to recent work by the author in which new partition type infinite products were derived. Also
recently, Baake et al [3] and Mosseri [14] considered the 2-D
visible lattice points as part of an optical
experiment in which the so-called Optical Fourier Transform was applied. Many of the techniques
espoused in Glasser and Zucker [11], and in Ninham et al [15] involving Mellin and Möbius inversions
are applicable also to the current paper. |
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| ISSN: | 0161-1712 1687-0425 |