Using the result (2.35), setting d = 4 + 2 ϵ and working in the MS renormalization scheme, J ( d ; 1 , m ; 1 , m ; 1 , 0) = m 2 (4 π ) 4 exp$^{[}$2 ϵ$^{(}$ log$^{[}$ m 2 µ 2 ] − γ$_{E}$$^{)]}$ Γ $^{2}$( − ϵ ) Γ (1 + ϵ ) Γ ( − 1 − 2 ϵ ) Γ (2 + ϵ ) Γ ( − 2 ϵ ) $_{4}$F$_{3}$$^{}$  − 1 − 2 ϵ , − ϵ , − ϵ , 1 2 + ϵ , − ϵ , 1 2 − ϵ w   , w = q 2 4 m 2 . (2.69) Because the $_{4}$F$_{3}$ hypergeometric function has one common upper and lower index, it reduces to a $_{3}$F$_{2}$ hypergeometric function. Using the series representation of the hypergeometric function, the result can be written as Noting that the factor multiplying the sum is O ( ϵ $^{0}$), we only need to expand the sum to this order. Also, note that the for n ≥ 2 we may safely set ϵ = 0 in the sum, so we can extract the n = 0 and n = 1 terms. Doing so, we have Letting k = n − 2 and using the properties of the Gamma function, the sum can be expressed as a hypergeometric function 74 w 2 ∞ ∑ k =0 Γ (1 + k ) Γ (2 + k ) Γ (3 + k ) Γ (4 + k ) Γ ( 5 2 + k ) w k Γ (3 + k ) = 2 w 2 9 √ π $_{3}$F$_{2}$$^{[}$ 1 , 1 , 2 ; 4 , 5 2 ; w$^{]}$ . (2.72) J ( d ; 1 , m ; 1 , m ; 1 , 0) = m 2 (4 π ) 4 exp$^{[}$2 ϵ$^{(}$ log$^{[}$ m 2 µ 2 ] − γ$_{E}$$^{)]}$ Γ ( − ϵ ) Γ$^{(}$ 1 2 − ϵ$^{)}$ $^{[}$Γ ( − 1 − 2 ϵ ) Γ ( − ϵ ) Γ (2 + ϵ ) Γ ( 1 2 − ϵ ) + Γ ( − 2 ϵ ) Γ (1 − ϵ ) Γ (3 + ϵ ) Γ ( 3 2 − ϵ $_{)}$w + ∞ ∑ n =2 Γ ( − 1 − 2 ϵ + n ) Γ ( − ϵ + n ) Γ (1 + n ) Γ (2 + ϵ + n ) Γ ( 1 2 − ϵ + n ) w n n ! ] . (2.71) J ( d ; 1 , m ; 1 , m ; 1 , 0) = m 2 (4 π ) 4 exp$^{[}$2 ϵ$^{(}$ log$^{[}$ m 2 µ 2 ] − γ$_{E}$$^{)]}$ Γ ( − ϵ ) Γ (1 + ϵ ) Γ ( 1 2 − ϵ ) Γ ( − 2 ϵ ) ∞ ∑ n =0 Γ ( − 1 − 2 ϵ + n ) Γ ( − ϵ + n ) Γ (1 + n ) Γ (2 + ϵ + n ) Γ ( 1 2 − ϵ + n ) w n n ! . (2.70)