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Gamma‐ray bursts (GRBs) are brief but intense emissions of soft gamma‐rays, mostly lasting from a few to a few thousand seconds. For these types of high‐energy transients, the isotropic‐equivalent‐energy ( E  iso ) function may be more scientifically meaningful than the GRB isotropic‐equivalent‐luminosity ( L  iso ) function, as the traditional luminosity function refers to steady emission much longer than a few thousand seconds. In this work we construct, for the first time, the isotropic‐equivalent‐energy function for a sample of 95 bursts with measured redshifts ( z ), and find an excess of high‐ z  GRBs. Assuming that the excess is caused by a GRB luminosity function evolution in a power‐law form, we find a cosmic evolution of , which is comparable to that between  L  iso  and  z , namely  (both 1σ). The evolution‐removed isotropic‐equivalent‐energy function can be reasonably fitted by a broken power law, in which the dim and bright segments are  and , respectively (1σ). The cosmic GRB formation rate increases quickly in the region of , remains approximately constant for , and finally decreases with a power index of −3.80 ± 2.16 for   z ≳4 , in good agreement with the cosmic star formation rate observed to date.

Gamma‐ray bursts: the isotropic‐equivalent‐energy function and the cosmic formation rate