• Corpus ID: 222379578

A shifted binomial theorem and trigonometric series

@article{Ouvry2020ASB,
  title={A shifted binomial theorem and trigonometric series},
  author={St'ephane Ouvry and Alexios P. Polychronakos},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
We introduce a shifted version of the binomial theorem, and use it to study some remarkable trigonometric integrals and their explicit rewriting in terms of binomial multiple sums. Motivated by the expressions of area generating functions arising in the counting of closed walks on various lattices, we propose similar sums involving fractional values of the area and show that they are closely related to their integer counterparts and lead to rational sequences converging to powers of $\pi$. Our… 

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