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The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm
We present a simple but efficient method of calculating Stieltjes constants at a very high level of precision, up to about 80 000 significant digits. This method is based on the hypergeometric-like expansion for the Riemann zeta function presented by one of the authors in 1997 [19]. The crucial i ...
Are the Stieltjes constants irrational? Some computer experiments
Khnichin’s theorem is a surprising and still relatively little known result. It can be used as a specific criterion for determining whether or not any given number is irrational. In this paper we apply this theorem as well as the Gauss-Kuzmin theorem to several thousand high precision (up to mo ...