In general, the Polylogarithm is defined recursively: which for n = 3 is called the Trilogarithm. The Dilogarithm satisfies the identity The Trilogarithm satisfies a similar identity, As mentioned previously, the Mathematica package HypExp can perform epsilon expansions of some generalized hypergeometric functions. This was used in the heavy-light diquark calculation in Chapter 4. However, when this package was used some functions with an inappropriate branch cut structure were generated. Using the identities (B.21) and (B.22), the functions with this branch structure can be canceled identically, and those that remain have the appropriate branch cut structure. Li$_{n}$ ( z ) = ∫ z 0 ds Li$_{n}$$_{−}$$_{1}$ ( s ) s , (B.20) Li$_{2}$ (1 − z ) = π 2 6 − log ( z ) log (1 − z ) − Li$_{2}$ ( z ) . (B.21) Li$_{3}$ (1 − z ) = π 2 6 log (1 − z ) + 1 6 log $^{3}$(1 − z ) − 1 2 log $^{2}$(1 − z ) log ( z ) − Li$_{3}$ ( z ) − Li$_{3}$$^{(}$ z z − 1$^{)}$ + ζ (3) . (B.22) 112