The error function, erf(x), represents a statistical function, but it can also be used as an integration trick in the case of complex exponentials, which occur fairly frequently in the study of physics, for example, in differential equations describing heat propagation. It is also used in quantum mechanics to describe particles represented by a wave function, and in astrophysics for the spectroscopic analysis of spectral lines, as in the examples discussed in detail (in english and italian translation).
Brussi 2026_The error function as an integration trick
Brussi 2026_La funzione di errore come trucco di integrazione
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