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math-ph2020
A shifted binomial theorem and trigonometric series
Stéphane Ouvry, Alexios P. Polychronakos
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.…
math-ph2020
Lattice walk area combinatorics, some remarkable trigonometric sums and Apéry-like numbers
Stéphane Ouvry, Alexios Polychronakos
Explicit algebraic area enumeration formulae are derived for various lattice walks generalizing the canonical square lattice walk, and in particular for the triangular lattice chir…