FeynCalc manual (development version)

SumT

SumT[1, m] is the alternative harmonic number i=1m(1)i/i\sum _{i=1}^m (-1){}^{\wedge}i/i

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

Overview, SumP, SumS.

Examples

SumT[1, m - 1]

S~1(m1)\tilde{S}_1(m-1)

SumT[2, m - 1]

S~2(m1)\tilde{S}_2(m-1)

SumT[1, m]

S~1(m)\tilde{S}_1(m)

SumT[1, m, Reduce -> True]

S~1(m1)+(1)mm\tilde{S}_1(m-1)+\frac{(-1)^m}{m}

SumT[1, 4]

712-\frac{7}{12}

SumT[1, 2, m - 1]

S~12(m1)\tilde{S}_{12}(m-1)

SumT[1, 2, 42]

3898795869705501336048986429870362142961015213868392710512121660702378405316004964483761080879190528000000-\frac{38987958697055013360489864298703621429610152138683927}{10512121660702378405316004964483761080879190528000000}

SumT[1, 4]

712-\frac{7}{12}

SumS[-1, 4]

712-\frac{7}{12}

SumT[1, 2, 12]

5756174365691321300003648000-\frac{57561743656913}{21300003648000}

SumS[1, -2, 42]

3898795869705501336048986429870362142961015213868392710512121660702378405316004964483761080879190528000000-\frac{38987958697055013360489864298703621429610152138683927}{10512121660702378405316004964483761080879190528000000}

Array[SumT, 6]

{1,58,179216,12071728,170603216000,155903216000}\left\{-1,-\frac{5}{8},-\frac{179}{216},-\frac{1207}{1728},-\frac{170603}{216000},-\frac{155903}{216000}\right\}

Array[SumS[-2, 1, #1] &, 6]

{1,58,179216,12071728,170603216000,155903216000}\left\{-1,-\frac{5}{8},-\frac{179}{216},-\frac{1207}{1728},-\frac{170603}{216000},-\frac{155903}{216000}\right\}