On unique existence theorem and exact solution formula of the inverse black-body radiation problem

The unique existence theorem of the inverse black-body radiation problem is proved. Its exact solution formula of closed form and some general Laurent expansions are derived. The Gaussian spectrum problem has been investigated numerically by many scientists, but its exact solution has not yet been obtained. The exact solution for the Gaussian spectrum problem is obtained by the derived exact solution formula and the criterion canceling divergence is described.<
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