The Birth and Early Developments of Orthogonal Polynomials

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 …