An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences

Details An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences

2011-05-15

arxiv.org/abs/1105.3399v1

Mathematics

General Mathematics

Scientific paper

We present an integral representation of Kekul\'{e} numbers for $P_{2} (n)$
benzenoids. Related integrals of the form $\int_{-\pi}^{\pi}
\frac{\cos(nx)}{\sin^{2}x +k} dx$ are evaluated. Conjectures relating double
integrals of the form $\int_{0}^{m} \int_{-\pi}^{\pi} \frac{\cos
(2nx)}{k+\sin^{2}x} dx dk $ to Smarandache sequences are presented.

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