Geodesic
Linearization coefficients for the Jacobi polynomials
Séminaire lotharingien de combinatoire, Tome 16 (1987) 
Dominique Foata; Doron Zeilberger. Linearization coefficients for the Jacobi polynomials. Séminaire lotharingien de combinatoire, Tome 16 (1987). http://geodesic.mathdoc.fr/item/SLC_1987_16_a0/
@article{SLC_1987_16_a0,
     author = {Dominique Foata and Doron Zeilberger},
     title = {Linearization coefficients for the {Jacobi} polynomials},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {1987},
     volume = {16},
     url = {http://geodesic.mathdoc.fr/item/SLC_1987_16_a0/}
}
TY  - JOUR
AU  - Dominique Foata
AU  - Doron Zeilberger
TI  - Linearization coefficients for the Jacobi polynomials
JO  - Séminaire lotharingien de combinatoire
PY  - 1987
VL  - 16
UR  - http://geodesic.mathdoc.fr/item/SLC_1987_16_a0/
ID  - SLC_1987_16_a0
ER  - 
%0 Journal Article
%A Dominique Foata
%A Doron Zeilberger
%T Linearization coefficients for the Jacobi polynomials
%J Séminaire lotharingien de combinatoire
%D 1987
%V 16
%U http://geodesic.mathdoc.fr/item/SLC_1987_16_a0/
%F SLC_1987_16_a0

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

The explicit non-negative representation of the linearization coefficients of the Jacobi polynomials obtained by Rahman seems to be difficult to be derived by combinatorial methods. However several combinatorial interpretations can be provided for the integral of the product of Jacobi polynomials and furnish an evaluation of this integral in the particular case where the subscript of the first polynomial is equal to the sum of the subscripts of the other polynomials. The following versions are available: