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            <title xml:lang="en">On the symmetry of Wigner (3-j) and Racah (6-j) coefficients</title>
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                <surname>Hage-Hassan</surname>
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                <forename>Mehdi</forename>
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                <title xml:lang="en">On the symmetry of Wigner (3-j) and Racah (6-j) coefficients</title>
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                    <surname>Hage-Hassan</surname>
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              <p>The Clebsh-Gordan coefficient formulas are determined using the integration of the product of three Wigner D-matrix. So we determine the generating function of these coefficients and the explicit expression of Van der Waerden formula for Wigner 3-j coefficient is derived simply. We also determine a new generating function of Wigner 6-j, by the coupling of three angular moments, and we derive without any difficulty Racah's formula for 6-j. We also propose a new method for the determination of the symmetries of the symbols 3-j and 6-j only from the expressions of these formulas. We also prove the connection of the coupling coefficients in bosons basis (Schwinger) and the analytic Fock space.</p>
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              <p>Les formules des coefficients des Clebsh-Gordan se déterminent à l’aide de la formule de l’intégration du produit de trois Wigner D-Matrix. Ainsi nous déterminons la fonction génératrice de ces coefficients  et la formule Van der Waerden. Nous déterminons aussi une nouvelle fonction génératrice de 6-j, par le couplage de trois moments angulaires, et la formule de 6-j de Racah. Nous proposons aussi une nouvelle méthode pour la détermination des  symétries des symboles 3-j et 6-j à partir des expressions de ces formules. Nous prouvons aussi la connexion de l’expression des coefficients des couplages dans l’espace des bosons (Schwinger)  et l’espace des fonctions analytiques de Fock.</p>
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