SumT[1, m] is the alternative harmonic number SumT[r, n] represents Sum[(-1)^i/i^r, {i,1,n}], SumT[r,s, n] is Sum[1/k^r (-1)^j/j^s, {k, 1, n}, {j, 1, k}].
See also: SumP, SumS.