H g ( M $^{)}$( x, ξ, t ) = ∞ ∑ n =1 odd n +1 ∑ l =0 even B g ( M ) n l ( t ) θ ( 1 − x 2 ξ 2 )( 1 − x 2 ξ 2 ) 2 C$^{5}$ 2 n − 1 ( x ξ ) $_{P}$′ l ( 1 ξ ) . (19) ˜ H $^{g}$( x, ξ, t ) = ∞ ∑ n =2 even n +1 ∑ l =1 odd ˜ B g $_{nl}$( t ) θ ( 1 − x 2 ξ 2 )( 1 − x 2 ξ 2 ) 2 C$^{5}$ 2 n − 1 ( x ξ ) $_{ξP}$′ l ( 1 ξ ) ; (20) ˜ H g ( PS $^{)}$( x, ξ, t ) = ∞ ∑ n =2 even n ∑ l =0 even ˜ B g ( PS ) nl ( t ) θ ( 1 − x 2 ξ 2 )( 1 − x 2 ξ 2 ) 2 C$^{5}$ 2 n − 1 ( x ξ ) P$_{l}$ ( 1 ξ ) . (21) h g ( E ) N,k ( t ) = N ∑ n =1 odd n +1 ∑ l =0 even B g ( E ) nl ( t )( − 1) k + l$_{−}$N$_{−}$ 1 2 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 ) . (23) 9 The set of coefficients h g ( E ) N,k ( t ) can be expressed through the generalized form factors B g ( E ) nl according to The partial wave expansion for the polarized gluon GPDs in the nucleon reads In fact, the most non-committal way to understand the partial wave expansions (18), (19), (20), (21) is to consider them just as formal series which satisfy the fundamental polynomiality property of gluon GPDs (9), (10). The summation procedure [15] allowing to convert these formal series into rigorously defined expressions is reviewed in the Appendix A. In what follows we are going to consider in details the properties of unpolarized gluon GPDs in the framework of the dual parametrization. The summary of results for the case of polarized gluon GPDs in the nucleon is presented in the Appendix B. Let us first consider the electric combination. For odd N the ( N − 1)th Mellin moment is indeed the polynomial of ξ of order N + 1 ∫ 1 0 dxx N − $^{1}$H g ( E $^{)}$( x, ξ, t ) = N +1 ∑ k =0 even ξ $^{k}$h g ( E ) N,k ( t ) = ξ N N ∑ n =1 odd n +1 ∑ l =0 even B g ( E ) nl ( t ) ξP$_{l}$ ( 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 ) . (22)