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The Dirac delta function and the Feynman propagator of the harmonicoscillator are found by a simple calculation using Fock Bargmann space and thegenerating function of the harmonic oscillator. With help of the Schwingergenerating function of Wigner's D-matrix elements we derive the generatingfunction of spherical harmonics, the quadratic transformations and thegenerating functions of: the characters of SU (2), Legendre and Gegenbauerpolynomials. We also deduce the van der Wearden invariant of 3-j symbols of SU(2). Using the Fock Bargmann space and its complex conjugate we find theintegral representations of 3j symbols, function of the series, and from theproperties of we deduce a set of generalized hypergeometric functions of SU (2)and from Euler's identity we find Regge symmetry. We find also the integralrepresentation of the 6j symbols. We find the generating function and a newexpression of the 3j symbols for SU (3) multiplicity free. Our formula of SU(3) is a product of a constant, 3j symbols of SU (2) by . The calculations inthis work require only the Gauss integral, well known to undergraduates.

On Fock-Bargmann space, Dirac delta function, Feynman propagator, angular momentum and SU(3) multiplicity free