SumS
SumS[1, m]
is the harmonic number S1(m)=∑i=1mi−1.
SumS[1,1,m]
is ∑i=1mS1(i)/i.
SumS[k,l,m]
is ∑i=1mSl(i)/ik.
SumS[r, n]
represents Sum[Sign[r]^i/i^Abs[r], {i, 1, n}]
.
SumS[r,s, n]
is Sum[Sign[r]^k/k^Abs[r] Sign[s]^j/j^Abs[s], {k, 1, n}, {j, 1, k}]
etc.
See also
Overview, SumP, SumT.
Examples
S1(m−1)
S2(m−1)
S−1(m)
SumS[1, m, Reduce -> True]
S1(m−1)+m1
SumS[3, m + 2, Reduce -> True]
S3(m+1)+(m+2)31
SetOptions[SumS, Reduce -> True];
SumS[3, m + 2]
m31+S3(m−1)+(m+1)31+(m+2)31
SetOptions[SumS, Reduce -> False];
SumS[1, 4]
1225
S12(m−1)
426000072960031276937512951
−127
−127