FeynCalc manual (development version)

SumS

SumS[1, m] is the harmonic number S1(m)=i=1mi1S_ 1(m) = \sum_ {i=1}^m i^{-1}.

SumS[1,1,m] is i=1mS1(i)/i\sum_{i=1}^m S_ 1 (i)/i.

SumS[k,l,m] is i=1mSl(i)/ik\sum_{i=1}^m 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.

See also

Overview, SumP, SumT.

Examples

SumS[1, m - 1]

S1(m1)S_1(m-1)

SumS[2, m - 1]

S2(m1)S_2(m-1)

SumS[-1, m]

S1(m)S_{-1}(m)

SumS[1, m, Reduce -> True]

S1(m1)+1mS_1(m-1)+\frac{1}{m}

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

S3(m+1)+1(m+2)3S_3(m+1)+\frac{1}{(m+2)^3}

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

1m3+S3(m1)+1(m+1)3+1(m+2)3\frac{1}{m^3}+S_3(m-1)+\frac{1}{(m+1)^3}+\frac{1}{(m+2)^3}

SetOptions[SumS, Reduce -> False]; 
 
SumS[1, 4]

2512\frac{25}{12}

SumS[1, 2, m - 1]

S12(m1)S_{12}(m-1)

SumS[1, 1, 1, 11]

312769375129514260000729600\frac{31276937512951}{4260000729600}

SumS[-1, 4]

712-\frac{7}{12}

SumT[1, 4]

712-\frac{7}{12}