Engineering and physics demand a through knowledge of applied mathematics and a good understanding of special functions. These functions commonly arise in such areas of applications as heat conduction, communication systems, electro-optics, approximation theory, probability theory, and electric circuit theory, among others. The subject of special functions is quite rich and expanding continuously with the emergence of new problems in the areas of applications in engineering and applied sciences. We investigate generalized gamma function, digamma function, the generalized incomplete gamma function, extended beta function. Also, some properties of these functions are taken into hand. Keywords: Approximation, Circuit, Gamma, Beta, Digamma