The study of fractals and their associated complex dimensions has led to the development of anew form of calculus. In [LvF13], Michel Lapidus and Machiel van Frankenhuijsen introduce two kinds of fractals, ordinary fractal strings and generalized fractal strings. Generalized fractal strings are locally compact measures taking place over the positive real line with mass near zero. In [LvF13], Lapidus and van Frankenhuijsen derive a way of recovering a generalized fractal string from it known complex dimensions via an explicit formula. In this thesis, we offer two key results which involve Taylor series expansions of fractals. The first result involves writing the explicit formula as a Taylor series, summing over the fractional derivatives of δ where the order is taken at the complex dimensions of the generalized fractal string. The second result is specific to more recent work done by Michel Lapidus and Claire David in [DL22a] and [DL22b]. This result involves the determination of coefficients of a fractal power series for the Weierstrass graph, mentioned in [DL22b]. Both results are important as they contribute to the development of fractal calculus. vi