˜ B g $_{nl}$( t ) as follows The expression for the polarized forward like function Δ G$_{0}$ through the t -dependent polarized gluon density Δ g ( y, t ) reads Finally, to sum up the formal series for ˜ H g ( P S ) (21) the set of polarized gluon forward like functions Δ G ( P S ) 2 ν ( y, t ) whose Mellin moments generate the generalized form factors ˜ B g $_{n l}$( t ). with n = 2 ν + l The resulting expression for ˜ H g through Δ G$_{2}$$_{ν}$ reads where ˜ H g ( P S ) ( ν $^{)}$( x, ξ, t ) defined for − ξ < x < 1 is given by 33 ˜ h g $_{N,k}$( t ) = N ∑ n =2 even n +1 ∑ l =1 odd ˜ B g $_{nl}$( t )( − 1) k + l$_{−}$N +1 2 ( − 1 + k − N ) Γ( 2 − k + l + N 2 ) 3 · 2 k $^{+1}$Γ( 1+ k + l − N 2 ) Γ(2 − k + N ) × n (1 + n ) (2 + n ) (3 + n ) Γ( N ) Γ( 2 − n + N 2 ) Γ( 5+ n + N 2 ) . (B20) Δ G$_{0}$ ( x, t ) = − 9 2 x 2 ∫ 1 x dy y $_{3}$Δ g ( y, t ) + 3 x ∫ 1 x dy y $_{2}$Δ g ( y, t ) + 3 2 ∫ 1 x dy y Δ g ( y, t ) . (B21) ˜ B g ( P S ) n n − 2 $_{ν}$( t ) = ∫ 1 0 dyy $^{n}$Δ G P S 2 ν ( y, t ) with n ≥ 2 , even . (B22) ˜ H g ( P S $^{)}$( x, ξ, t ) = ∞ ∑ ν =0 ξ 2 ν 2 [ ˜ H g ( P S ) ( ν $^{)}$( x, ξ, t ) − ˜ H g ( P S ) ( ν $^{)}$( − x, ξ, t ) ] , (B23) ˜ H g ( P S ) ( ν $^{)}$( x, ξ, t ) = θ ( x > ξ ) 1 π ∫ 1 y$_{0}$ dy [ 1 3 ( 1 − y ∂ ∂y + 1 2 y 2 ∂ 2 ∂y 2 ) Δ G ( P S ) 2 ν ( y, t ) ] ∫ s$_{2}$ s$_{1}$ ds x 1 − 2 ν s (1 − s $^{2}$) √ 2 x$_{s}$ − x 2 s − ξ 2 + θ ( | x | < ξ ) 1 π 1 0 dy 1 3 1 − y ∂ ∂y + 1 2 y 2 ∂ 2 ∂y 2 Δ G ( P S ) 2 ν ( y, t ) ] { ∫ s$_{3}$ s$_{1}$ ds x 1 2 ν s (1 − s $^{2}$) 2 x$_{s}$ − x 2 s − ξ 2 − π ξ 2 ν ( 1 − x 2 ξ 2 ) 2 2 ν − 2 ∑ l =0 C$^{5}$ 2 2 ν − l − 2 ( x ξ ) P$_{l}$ ( 1 ξ ) 6 y 2 ν − l − 1 (2 ν − l + 1)(2 ν − l + 2) } . (B24)