information:extraction, structural:expansion
Analysis

In 1857, Boole published the treatise "On the Comparison of Transcendent, with Certain Applications to the Theory of Definite Integrals", in which he studied the sum of residues of a rational function. Among other results, he proved what is now called Boole's identity:

for any real numbers a > 0, b, and t > 0. Generalisations of this identity play an important role in the theory of the Hilbert transform.