Three classic improper integrals all collapse to √π or π
elonmusk · x · 2026-07-23
Three classic improper integrals have elegant closed forms: the Gaussian integral equals √π, the Lorentzian integral equals π, and the sinc integral also equals π.
The post highlights that these identities are tied to techniques like contour integration, and notes a practical engineering use: the sinc integral appears in the sampling theorem for reconstructing continuous-time signals from discrete samples.
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