FeynCalc manual (development version)

SumP

SumP[k, m] is 2^{k-1}\sum _{i=1}^{2m}\left(1+(-1)^i\right)/i^k.

See also

Overview, SumS, SumT.

Examples

SumP[1, m - 1]

S_1^{'(m-1)}

SumP[2, m - 1]

S_2^{'(m-1)}

SumP[1, m]

S_1^{'(m)}

SumP[1, 4]

\frac{25}{12}

Explicit[SumP[1, n/2]] 
 
% /. n -> 8

\frac{1}{2} \left(1-(-1)^n\right) S_1\left(\frac{n-1}{2}\right)+\frac{1}{2} \left((-1)^n+1\right) S_1\left(\frac{n}{2}\right)

\frac{25}{12}