  In this paper we present the analytical calculations to derive the magnetic
field of a solenoid by solving exactly a fractional integral with the use of a
novel method. Starting from the Biot-Savart law, we consider a coil of
negligible thickness with a stationary electric current. We derive the
expressions of the on and off-axes magnetic field components. The results have
been compared to some simplified and known analytical formulae as well as to a
commercial numerical code showing a good agreement.
