Frobenius Solution for Legendre's Equation, Rodrigue's Formula and Normalization

The Frobenius solution to Legendre/s equation is developed in detail as is Rodrigue's formula, which is employed to normalize Legendre polynomials.

Legendre Polynomials and Angular Momentum

An introduction to Legendre polynomials as precursor to studying angular momentum in quantum chemistry,

Continued Fraction Solutions to Hermite's, Legendre's and Laguerre's Differential Equation

The continued fraction method for solving differential equations is illustrated using three famous differential equations used in quantum chemistry.

Legendre Polynomials, Dipole Moments, Generating Functions, etc..

A standard treatment of aspects of Legendre polynomials is treated here, including the dipole moment expansion, generating functions, etc..

A Universal Formula for Continuous Utility

A single formula assigns a continuous utility function to every representable preference relation.