A solution to an open problem on the Euler-Mascheroni constant

作者：Gavrea Ioan; Ivan Mircea^*

来源：Applied Mathematics and Computation, 2013, 224: 54-57.

DOI：10.1016/j.amc.2013.08.046

• Euler-Mascheroni constant
• Bernoulli numbers
• Le Verrier method
• Harmonic number

The classical Le Verrier algorithm for the calculation of the characteristic polynomial of a matrix has led us to a solution of an open problem concerning the Euler-Mascheroni constant gamma. More exactly, we prove that there exists uniquely a sequence of rational numbers (l(n))(n >= 1) such that, for any integer q >= 1, the sequence
Sigma(n)(k=1)1/k - log n - log (1 + l(1)/n + ... + l(q)/n(q)),
is an n(-q-1) order approximation of gamma.

• 出版日期2013-11-1