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A generalization of Lerch’s formula

Nobushige Kurokawa, Masato Wakayama (2004)

Czechoslovak Mathematical Journal

We give higher-power generalizations of the classical Lerch formula for the gamma function.

A recovery of Brouncker's proof for the quadrature continued fraction.

Sergey Khrushchev (2006)

Publicacions Matemàtiques

350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/π. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis' remarks presented in his Arithmetica Infinitorum. We show that Brouncker's and Wallis' formulas can be extended to MacLaurin's sinusoidal spirals via related Euler's products. We derive Ramanujan's...

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