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arXiv · 1105.3399

An Integral Representation of Kekul\'e Numbers, and Double Integrals Related to Smarandache Sequences

John M. Campbell
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Abstract

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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John M. Campbell. 2011-05-15. An Integral Representation of Kekul\'e Numbers, and Double Integrals Related to Smarandache Sequences. https://arxiv.org/abs/1105.3399

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