<< MB.m

<< AMBRE.m

Fullintegral[{1}, {PR[k1, 0, n1] PR[k1 + p1, 0, n2] 
            PR[k2 - k1, 0, n3] PR[k2, 0, n4] PR[k4, 0, n5] 
            PR[k2 + k4 + p1, 0, n6] PR[k3, 0, n7] PR[k3 - k2 - k4, 0, n8] 
            PR[k3 + p1, 0, n9]}, {k1, k3, k4, k2}];

invariants = {p1^2 -> s};

IntPart[1]

SubLoop[integral]

IntPart[2]

SubLoop[integral]

IntPart[3]

SubLoop[integral]

IntPart[4]

repr = SubLoop[integral];

BarnesLemma[repr, 1]

repr = %  /. {n1 -> 1, n2 -> 1, n3 -> 1, n4 -> 1, 
          n5 -> 1, n6 -> 1, n8 -> 1, n7 -> 1, 
          n9 -> 1}

rules = MBoptimizedRules[repr, eps -> 0, {}, {eps}]

integrals = 
      MBcontinue[repr, eps -> 0, rules, 
        Verbose -> False]

ser0 = 
        MBexpand[{integrals}, 
          Exp[4*eps EulerGamma], {eps, 0, 0}];

MBintegrate[ser0, {s -> -1/2}, Verbose -> False] // 
      AbsoluteTiming

441/8 Zeta[7]/s /. s -> -1/2 // N

MBintegrate[ser0, {s -> -1/7}]

441/8 Zeta[7]/s /. s -> -1/7 // N

ser = 
        MBexpand[{integrals}, 
          Exp[4*eps EulerGamma], {eps, 0, 2}];

MBintegrate[ser, {s -> -1/2}, Verbose -> False] // 
      AbsoluteTiming