A function f:C→C is said to be holomorphic at a point if there is some neighborhood around that point on which function is differentiable.
The function f:C→C is said to be analytic at a point if around that point there is a neighborhood on which f can be represented Taylor series expansion which converges to f. I have seen these definitions from Wikipedia but haven't seen in any book ,so can anybody provide me reference of a standard book where I can find the same definitions. Secondly how the concept of holomorphicity and analyticity coincides in complex analysis?which class is bigger in general? Thanks in advanced.
You can find them in Reinhold Remmert's Theory of complex functions or in Serge Lang's Complex Analysis, for instance. In those textbooks you will also find a proof of the fact that every holomorphic function is analytic, a highly non-trivial fact. On the other hand, it is quite easy to prove that every analytic function is holomorphic.