Infinite series can converge in various ways to give the resultant function. Particularly, here, we consider the Fourier series and compare it with its Taylor equivalent both of which are convergent infinite series in their own rights. However, these are valid under separate limiting conditions. We consider what happens if we try to derive one series from the other or see if such a derivation is possible at all and its implications. An expansion of the Dirichlet kernel, while using a form of the Dirac delta function has been shown to yield the Taylor series in its form. However, it introduced certain restrictions on both the local and global nature of such a function.