A preface to the reader
A recovery of Brouncker's proof for the quadrature continued fraction.
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...
About one problem of Bernoulli and Euler from the theory of statistical estimation.
We consider some results by D. Bernoulli and L. Euler on the method of maximum likelihood in parametric estimation. The statistical analysis is made by considering a parametric family with a shift parameter.