A339802 Decimal expansion of the imaginary part of harmonic number H(1/2 + i*sqrt(3)/2) where i=sqrt(-1).

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

Offset: 0

Author

Artur Jasinski, Dec 17 2020

Keywords

• nonn
• cons

Comments

For real part of H(1/2 + i*sqrt(3)/2) see A339801.

Examples

			0.691215820928755403365848...
		

Crossrefs

Cf. A256919, A338815, A339135, A339529, A339530, A339605, A339605, A339606, A339801.

Programs

Mathematica

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

Formula

Equals (Pi/2)*tanh(Pi*sqrt(3)/2) - sqrt(3)/2.

Equals Im(Psi(3/2 + i*sqrt(3)/2)).

Equals -sqrt(3)/2 + Im(Psi(1/2 + i*sqrt(3)/2)).

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