Geometric Properties Of Tau-Confluent Hypergeometric Function

In the present investigation we first introduce normalized tau-confluent hypergeometric function phi(tau)(a; b; z) and then find sufficient conditions so that phi(tau)(a; b; z) have certain geometric properties like close-to-convexity and starlikeness in the open unit disk D. Upper bound of vertical bar phi(tau)(a; b; z)vertical bar and vertical bar phi(tau)(a; b; z)'vertical bar are also determined.