The Birth and Early Developments of Orthogonal Polynomials: A Chronological History

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. This 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.