A339802 -id:A339802 - cp's OEIS frontend

A339801 Decimal expansion of the real part of harmonic number H(1/2 + i*sqrt(3)/2), where i=sqrt(-1).

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, 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, 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

Offset: 0

Artur Jasinski, Dec 17 2020

For imaginary part see A339802.

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

			0.862289106171836386535085450...

Wikipedia, Digamma function

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

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

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.
Equals -1/2 + 3*A339604 + 3*A339606.
Equals Re((1 + i*sqrt(3))*Sum_{k>=0} 1/((1 + k)*(3 + i*sqrt(3) + 2*k))).

cp's OEIS Frontend

A339801 Decimal expansion of the real part of harmonic number H(1/2 + i*sqrt(3)/2), where i=sqrt(-1).

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