For even N the polynomiality condition (10) require that The coefficients ˜ h g ( PS ) N,k ( t ) at powers of ξ in (B25) are given by The expression for the pseudoscalar forward like function Δ G ( PS ) 0 through the pseudoscalar combination of t -dependent polarized gluon densities g ( PS $^{)}$( y, t ) ≡ Δ g ( y, t )+ τ Δ e $^{g}$( y, t ) reads ∫ 1 0 dxx N − 1 ˜ H g ( PS $^{)}$( x, ξ, t ) = N ∑ k =0 even ξ k ˜ h g ( PS ) N,k ( t ) = ξ N N ∑ n =2 even n ∑ l =0 even ˜ B g ( PS ) nl ( t ) P$_{l}$ ( 1 ξ ) n (1 + n ) (2 + n ) (3 + n ) Γ( 5 $_{2}$) Γ( N ) 9 · 2 N Γ(1 + − n + N 2 ) Γ( 7 2 + − 2+ n + N 2 ) . (B25) ˜ h g ( PS ) N,k ( t ) = N ∑ n =2 even n ∑ l =0 even ˜ B g ( PS ) nl ( t )( − 1) k + l$_{−}$N 2 Γ( 1 − k + l + N 2 ) 3 · 2 k $^{+2}$Γ( 2+ k + l − N 2 ) Γ(1 − k + N ) × n (1 + n ) (2 + n ) (3 + n ) Γ( N ) Γ( 2 − n + N 2 ) Γ( 5+ n + N 2 ) . (B26) Δ G ( PS ) 0 ( x, t ) = 45 2 x 2 ∫ 1 x dy y $_{3}$Δ g ( PS $^{)}$( y, t ) − 9 x ∫ 1 x dy y $_{2}$Δ g ( PS $^{)}$( y, t ) − 3 2 ∫ 1 x dy y Δ g ( PS $^{)}$( y, t ) . (B27) [1] D. Mueller, D. Robaschik, B. Geyer, F.M. Dittes, and J. Horejsi, Fortschr. Phys. 42 , 101 (1994); A. V. Radyushkin, Phys. Lett. B 380 (1996) 417 [arXiv:hep-ph/9604317]; X. D. Ji, Phys. Rev. D 55 (1997) 7114 [arXiv:hep-ph/9609381]; J. C. Collins, L. Frankfurt and M. Strikman, Phys. Rev. D 56 (1997) 2982 [arXiv:hep- ph/9611433]. [2] X. D. Ji, Phys. Rev. Lett. 78 (1997) 610 [arXiv:hep-ph/9603249]. [3] K.Goeke, M.V.Polyakov and M.Vanderhaeghen, Progr. Part. Nucl. Phys. Vol.47, No 2, 401-515 (2001) [arXiv:hep-ph/0106012]. [4] M. Diehl, Phys. Rept. 388 , 41 (2003) [arXiv:hep-ph/0307382]. [5] A.V. Belitsky and A. V. Radyushkin, Phys. Rept. 418 , 1 (2005), [arXiv:hep-ph/0504030]. [6] S. Boffi and B. Pasquini, Riv. Nuovo Cim. 30 , 387 (2007) [arXiv:0711.2625 [hep-ph]]. 34