Double series for $π$ and their $q$-analogues

Published 4 Oct 2022 in math.CO | (2210.01331v1)

Abstract: With the help of the partial derivative operator and several summation formulas for hypergeometric series, we find three double series for $\pi$. In terms of the operator just stated and several summation formulas for basic hypergeometric series, we also establish $q$-analogues of these double series.

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