Point ξ = x The important limiting case in which the expressions (28), (29) are reduced to much simpler forms is the point x = ξ . Point ξ = 1 Another notable limiting case is ξ = 1: and Forward limit and G ( E,M ) 0 ( x, t ) Let us introduce the convenient notations for the combinations of the t -dependent parton densities to which GPDs H g ( E,M ) are reduced in the limit ξ → 0: 12 H g ( E $^{)}$( ξ, ξ, t ) = 2 3 π ξ ∫ 1 1$_{−}$ √ 1$_{−}$ ξ 2 ξ dy y ∞ ∑ ν =0 y 2 $^{ν}$G ( E ) 2 ν ( y, t ) [ 1 √ 2 y ξ − y 2 − $_{1}$] ; H g ( M $^{)}$( ξ, ξ, t ) = − ξ 2 ∂ ∂ξ 2 3 π ∫ 1 1$_{−}$ √ 1$_{−}$ ξ 2 ξ dy y ∞ ∑ ν =0 y 2 $^{ν}$G ( M ) 2 ν ( y, t ) [ 1 √ 2 y ξ − y 2 − $_{1}$] . (31) H g ( E $^{)}$( x, ξ = 1 , t ) = 1 2 (1 − x $^{2}$)2 ∞ ∑ ν =0 ∫ 1 0 dyy [ 1 (1 − 2 xy + y $^{2}$) 5 2 + 1 (1 + 2 xy + y $^{2}$) 5 2 − 2$^{2}$$^{ν}$ − 2 ∑ j =0 even y j C$^{5}$ 2 j ( x )   G ( E ) 2 ν ( y, t ) ; (32) H g ( M $^{)}$( x, ξ = 1 , t ) = 1 2 (1 − x $^{2}$)2 ∞ ∑ ν =0 ∫ 1 0 dy [ 1 (1 − 2 xy + y $^{2}$) 5 2 + 1 (1 + 2 xy + y $^{2}$) 5 2 − 2$^{2}$$^{ν}$ − 2 ∑ j =0 even y j C$^{5}$ 2 j ( x )   y 3 − 2 ν ∂ ∂y ( y 2 ν ∂ ∂y G ( M ) 2 ν ( y, t ) ) . (33) H g ( E $^{)}$( x, ξ = 0 , t ) = xg ( x, t ) + τxe $^{g}$( x, t ) ≡ xg ( E $^{)}$( x, t ) ; H g ( M $^{)}$( x, ξ = 0 , t ) = xg ( x, t ) + xe $^{g}$( x, t ) ≡ xg ( M $^{)}$( x, t ) , (34)