Exact closed‐form expressions for the Fresnel region electric and magnetic fields of circular loop and annular slot antennas are given in terms of the functionsen(&sgr;,&ggr;)=(1/2&pgr;)02&pgr; cos(n&PHgr;) sin[&sgr;(1–2&ggr; cos&PHgr;)1/2] d&PHgr;andfn(&sgr;,&ggr;)=(1/2&pgr;)02&pgr; cos(n&PHgr;) cos[&sgr;(1–2&ggr; cos&PHgr;)1/2] d&PHgr;,where ‐ ∞ < &sgr; < ∞ and 0 ≤ &ggr; ≤ 1/2. For a circular loope antenna with a constant current distribution the Fresnel region fields are obtained in terms of the functionsqn(&sgr;,&ggr;)=fn(&sgr;,&ggr;)+ien(&sgr;,&ggr;), withn=0,1, and 2, and for a cosine current distribution the Fresnel region fields are obtained in terms of the functionsqn(&sgr;,&ggr;), withn=0,1,2,3, and 4. The magnetic field of an annular slot antenna excited by a constant voltage is expressed exactly in terms of an infinite series involving the functionsqn(&sgr;,&ggr;). The Fresnel region magnetic field of the annular slot antenna is simply given in terms ofq1(&sgr;,&ggr;). The functionsqn(&sgr;,&ggr;) permitted a simple evaluation of the electric and magnetic field strength in the Fresnel region. The functionsqn(&sgr;,&ggr;) forn=0,1,2,3, and 4 are tabulated for values of &sgr;=0.5, 1, 2, 5, 10, 25, and 50 and values of &ggr; from 0.01 to 0.5.