Abstract: The disk coils are the core element of energy coupling of the wireless power transmission system blooming in recent years. By introducing generalized hypergeometric functions _pF_q, the integral expression of self-inductance of disk coils is transformed into a closed form. Similarly, the closed form expression of mutual inductance of coaxial coplanar disk coils is obtained by establishing a relationship between the complete elliptic integrals and generalized hypergeometric functions. These closed form solutions can bypass the numerical integration of traditional methods for the inductance calculations. Furthermore, based on the obtained closed form solution the GPW (given piece of wire) optimization problem is analyzed and the maximum value of self-inductance is found for disk coils which are wound by a piece of given wire. It is also revealed that the ratio of the outer and inner radii of the optimal disk coils is independent of the geometric parameters of winding wires. Numerical results show the high consistency between existing methods and methods proposed in this paper.