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'William Brouncker, 2nd Viscount Brouncker', FRS (1620 – 5 April 1684) was an English mathematician.
Brouncker obtained a PhD at the University of Oxford in 1647. He was one of the founders and the first President of the Royal Society. In 1662, he became Chancellor to Queen Catherine, then chief of the Saint Catherine hospital. His mathematical work concerned in particular the calculations of the lengths of the parabola and cycloid, and the quadrature of the hyperbola, which requires approximation of the natural logarithm function by infinite series. He was the first in England to take interest in generalised continued fractions and, following the work of John Wallis, he provided development in the generalised continued fraction of pi.

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Brouncker's formula

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Brouncker's formula

This formula provides a development in generalized continued fraction of π:

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