SumS

Description

SumS[1, m] is the harmonic number (∑_(i = 1)^m) i^(-1) (=(Subscript[S, 1])(m) ). SumS[1,1,m] is (∑_(i = 1)^m) (Subscript[S, 1])(i)/i. SumS[k,l,m] is (∑_(i = 1)^m) (Subscript[S, l])(i)/(i^k). 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.

Options[SumS]

See also:  SumP, SumT.

Examples

SumS[1, m - 1]

SumS[2, m - 1]

SumS[-1, m]

SumS[1, m, Reduce -> True]

SumS[3, m + 2, Reduce -> True]

SetOptions[SumS, Reduce -> True];

SumS[3, m + 2]

SetOptions[SumS, Reduce -> False];

SumS[1, 4]

(∑_(i = 1)^4) 1/i

SumS[1, 2, m - 1]

SumS[1, 1, 1, 11]

SumS[-1, 4]

SumT[1, 4]