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Very recently a new series representation of Humbert's double hypergeometricseries $\Phi_3$ in series of Gauss's $_2F_1$ function was given by one of us.The aim of this short research note is to provide an alternative proof of theresult. A few interesting special cases are also given.

On a representation of Humbert's double hypergeometric series $\Phi_3$ in a series of Gauss's $_2F_1$ function