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math.NT2023
The computation of , and beyond by using telescoping series
Óscar Ciaurri, Luis M. Navas, Francisco J. Ruiz +1
We present some simple proofs of the well-known expressions for \[ ζ(2k) = \sum_{m=1}^\infty \frac{1}{m^{2k}}, \qquad β(2k+1) = \sum_{m=0}^\infty \frac{(-1)^m}{(2m+1)^{2k+1}}, \] w…
math.NT2023★ 7 cited
Three essays on Machin's type formulas
Armengol Gasull, Florian Luca, Juan L. Varona
We study three questions related to Machin's type formulas. The first one gives all two terms Machin formulas where both arctangent functions are evaluated -integers, that is va…