Computes sign-alternating reciprocal harmonic sums
AlternatingHarmonicNumber[n]
AlternatingHarmonicNumber[n, r]
AlternatingHarmonicNumber[n, r, s]
Table[AlternatingHarmonicNumber[n], {n, 10}]
→ {1, 1/2, 5/6, 7/12, 47/60, 37/60, 319/420, 533/840, 1879/2520, 1627/2520}Series[AlternatingHarmonicNumber[x], {x, 0, 3}]
→ SeriesData[x, 0, {Derivative[1][AlternatingHarmonicNumber][0], Derivative[2][AlternatingHarmonicNumber][0]/2, Derivative[3][AlternatingHarmonicNumber][0]/6}, 1, 4, 1]ReImPlot[AlternatingHarmonicNumber[t], {t, 0, 5}]
→ -Graphics-