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We derive product and series representations of the gamma function usingNewton interpolation series. Using these identities, a new formula for thecoefficients in the Taylor series of the reciprocal gamma function is found. Wealso find two new series representations for the Euler-Mascheroni constant,containing only rational terms. After that, we introduce a new pseudogammafunction which we call the $\Lambda$ function. This function interpolates thefactorial at the positive integers, the reciprocal factorial at the negativeintegers, and is convergent for the entire real axis. Finally, we conjecture anovel series representation for the principal branch of the inverse gammafunction $\text{inv}\Gamma_0(z)$.

Series and Product Representations of Gamma, Pseudogamma and Inverse Gamma Functions