In 1805, Legendre published the first description of the method of least squares as an algebraic fitting procedure. It was subsequently justified on statistical grounds by Gauss and Laplace.

Legendre, a French mathematician who was born in Paris in 1752 and died there in 1833, made major contributions to number theory, elliptic integrals before Abel and Jacobi, and analysis.

The ordinary differential equation referred to as Legendre’s differential equation is frequently encountered in physics and engineering. In particular, it occurs when solving Laplace’s equation in …

The portion of the work translated here is found on pages 72–75. Adrien-Marie Legendre (1752–1833) was for five years a professor of mathematics in the ́Ecole Militaire at Paris, and his early studies on …

1. Legendre equation: series solutions The Legendre equation is the second order differential equation (1) (1 x2)y′′ 2xy′ + λy = 0 − which can also be written in self-adjoint form as

Legendre functions are important in physics because they arise when the Laplace or Helmholtz equations (or their generalizations) for central force problems are separated in spherical coordinates.

These polynomials are used in solving problems with spherical symmetry, such as in quantum mechanics and electromagnetism. Physics: Used in solving Laplace’s equation in spherical …