Michela Redivo-Zaglia – författare

The shape of the Earth was a significant scientific question in the eighteenth century. When it was discovered that the Earth was flattened at the poles, scientists sought to understand the cause, leading to the study of the gravitational attraction of celestial spheroids. The solution drew upon Newton’s law of universal gravitation, which used the distance between two bodies based on the law of cosines. Expanding the inverse of this distance into a power series naturally leads to a class of orthogonal polynomials. These were introduced by Legendre and, a little bit later, by Laplace. Legendre was the first to prove their orthogonality. Thirty years later, Gauss, approaching the problem from the perspective of numerical quadrature, independently arrived at the same polynomials. Over time, as concern for the gravitational problem of spheroids waned, the intrinsic mathematical interest in orthogonal polynomials took precedence.The Birth and Early Developments of Orthogonal Polynomials: A Chronological History is the first book to describe the history of orthogonal polynomials, covering their birth and early developments from the end of the 18th century to the middle of the 20th century. It includes biographies of principal and lesser-known figures, anecdotes, and accounts of the countries and institutions involved.The book will appeal to researchers and students in applied mathematics, mathematical analysis, special functions, and orthogonal polynomials as well as to those interested in the history of mathematics and the sciences.

This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects.A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.