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The present monograph consists, in a concise way, of numerical algorithms as well as theoretical formulas that involve Euler's gamma function and psi (or digamma) function, the author has developed during the period 2003-2012: the main bulk of this work-some results being unpublished-is an individual research, especially when it comes to applications within the frame of computational mathematics. We have also included some joint work applications, all mentioned in our bibliography since all joint research papers have been published in various math journals.