A documented account of how Euler worked, what he anticipated, where he erred, and what his methods could not achieve, with several new derivations from his formulas.
Some new series for $1/\pi$ and related congruences
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abstract
In this paper we prove some new series for $1/\pi$ as well as related congruences. We also raise several new kinds of series for $1/\pi$ and present some related conjectural congruences involving representations of primes by binary quadratic forms.
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Eulers Horizonte -- M\"oglichkeiten und Grenzen seiner Arbeitsweise in der Mathematik
A documented account of how Euler worked, what he anticipated, where he erred, and what his methods could not achieve, with several new derivations from his formulas.