epsilon expansion, the result for this integral is where Li$_{2}$ ( z ) denotes the dilogarithm function (B.18). Polylogarithm functions often ap- pear when hypergeometric functions such as (2.62) are expanded. Note the divergent terms proportional to ϵ − 2 and ϵ − $^{1}$. In a QCD sum rule calculation most of these terms would corre- spond to dispersion relation subtraction constants that would be eliminated when the Borel transform is applied. However, the divergent term proportional to log [1 − z ] is a non-local divergence that will not be eliminated by the Borel transform. Such a divergence must be dealt with through renormalization. Using the same method as was used to expand the integral (2.62), the epsilon expansion can be performed for all of the integrals that occur in Chapter 4, and for all those in Ref. [66]. Ref. [68] provides a result for the epsilon expansion of the $_{2}$F$_{1}$ hypergeometric function up to fifth order in epsilon. In conjunction with hypergeometric function identities, this result has be used to verify the results in Chapter 4 and in Ref. [66]. In addition, the Mathematica package HypExp [62, 63] can perform epsilon expansions of many different hypergeometric functions. This package has also been used to verify the results in Chapter 4 and Ref. [66]. Finally, we will consider a typical integral occurring in the hybrid calculations in Chap- ter 3, 73 J ( d ; 1 , m ; 1 , m ; 1 , 0) = 1 µ 2( d − 4) ∫ d $^{d}$k$_{1}$ (2 π ) d ∫ d $^{d}$k$_{2}$ (2 π ) d 1 ( k 2 1 − m $^{2}$) [ ( k$_{2}$ − q ) 2 − m 2 ] ( k$_{1}$ − k$_{2}$ ) 2 . (2.68) V ( d ; 1 , m ; 1 , 0 ; 1 , 0 ; 1 , 0) = 1 512 π 4 [ − 1 ϵ 2 + 1 ϵ ( 5 + 2 log [1 − z ] z − 2 log$^{[}$ m 2 µ 2 ]) − 1 2 ( 38 + π 2 − 20 log$^{[}$ m 2 µ 2 ] + 4 log 2 $^{[}$m 2 µ 2 ]) + 2 log [1 − z ] z ( 2 log$^{[}$ m 2 µ 2 ] − 5$^{)}$ +2$^{(}$1 + 1 z$^{)}$ Li$_{2}$ ( z ) +$^{(}$1 − 3 z$^{)}$ log $^{2}$[1 − z ]$^{]}$ , (2.67)