A339801 - OEIS

%I #38 Jan 15 2021 21:22:22

%S 8,6,2,2,8,9,1,0,6,1,7,1,8,3,6,3,8,6,5,3,5,0,8,5,4,5,0,0,5,4,4,2,9,8,

%T 5,7,1,6,6,2,1,1,1,4,6,1,0,1,1,4,9,8,5,0,2,9,5,6,4,4,0,3,5,2,7,9,5,6,

%U 5,7,6,2,3,3,2,8,8,5,1,0,1,4,2,9,3,6,7,0,0,9,1,8,7,7,9,0,1,2,7,7,4,5,3,2,8

%N Decimal expansion of the real part of harmonic number H(1/2 + i*sqrt(3)/2), where i=sqrt(-1).

%C For imaginary part see A339802.

%C For real b, Im(Psi(1/2 + b*i)) = Pi*tanh(Pi*b)/2, but no such closed formula is known for the real part (see Wikipedia link). - _Vaclav Kotesovec_, Dec 19 2020

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>

%F Equals 1/2 + gamma + Re(Psi(1/2 + i*sqrt(3)/2)), where gamma is the Euler-Mascheroni constant (see A001620) and Psi is the digamma function.

%F Equals -1/2 + 3*A339604 + 3*A339606.

%F Equals Re((1 + i*sqrt(3))*Sum_{k>=0} 1/((1 + k)*(3 + i*sqrt(3) + 2*k))).

%e 0.862289106171836386535085450...

%t RealDigits[N[Re[HarmonicNumber[1/2 + I Sqrt[3]/2]], 105]][[1]]

%Y Cf. A256919, A338815, A339135, A339529, A339530, A339604, A339605, A339606, A339802.

%K nonn,cons

%O 0,1

%A _Artur Jasinski_, Dec 17 2020