A363538 Decimal expansion of Sum_{k>=1} (H(k) - log(k) - gamma)/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number and gamma is Euler's constant (A001620).
7, 2, 8, 6, 9, 3, 9, 1, 7, 0, 0, 3, 9, 3, 0, 6, 0, 5, 9, 3, 7, 6, 0, 5, 8, 9, 1, 0, 2, 0, 2, 9, 1, 8, 0, 0, 4, 1, 7, 5, 0, 2, 7, 1, 8, 8, 1, 2, 9, 2, 2, 2, 9, 9, 8, 9, 1, 3, 6, 9, 0, 0, 5, 4, 2, 5, 2, 7, 2, 2, 7, 1, 9, 2, 5, 2, 3, 3, 5, 8, 6, 9, 6, 4, 2, 6, 9, 7, 4, 4, 2, 3, 8, 8, 6, 5, 3, 7, 8, 6, 0, 4, 5, 5, 9
Offset: 0
Examples
0.72869391700393060593760589102029180041750271881292...
Links
- Iaroslav V. Blagouchine, Expansions of generalized Euler's constants into the series of polynomials in Pi^(-2) and into the formal enveloping series with rational coefficients only, Journal of Number Theory, Vol. 158 (2016), pp. 365-396.
- Ovidiu Furdui, Problem 844, Problems and Solutions, The College Mathematics Journal, Vol. 38, No. 1 (2007), p. 61; Infinite sums and Euler's constant, Solution to Problem 844, ibid., Vol. 39, No. 1 (2008), pp. 71-72.
Programs
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Mathematica
RealDigits[-StieltjesGamma[1] - EulerGamma^2/2 + Pi^2/12, 10, 120][[1]]
Formula
Equals -gamma_1 - gamma^2/2 + Pi^2/12, where gamma_1 is the 1st Stieltjes constant (A082633).