====== TTP02-39 The analytic value of a 3-loop sunrise graph in a particular kinematical configuration ======
 
 
   <hidden TTP02-39  The analytic value of a 3-loop sunrise graph in a particular kinematical configuration > We consider the scalar integral associated to the 3-loop sunrise graph
 with a massless line, two massive lines of equal mass $M$, a fourth line of
 mass equal to $Mx$, and the external invariant timelike and equal to the
 square of the fourth mass. We write the differential equation in $x$
 satisfied by the integral, expand it in the continuous dimension $d$
 around $d=4$ and solve the system of the resulting chained differential
 equations in closed analytic form, expressing the solutions in terms of
 Harmonic Polylogarithms. As a byproduct, we give the limiting values of
 the coefficients of the $(d-4)$ expansion at $x=1$ and $x=0$.
 </hidden>
|**P. Mastrolia, E. Remiddi**  | 
|**  Nucl.Phys.B  657 397-406 2003  **  |
| {{preprints:2002:ttp02-39.pdf|PDF}} {{preprints:2002:ttp02-39.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/0211451|arXiv]]   |
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