More Special Functions

This chapter surveys a number of sets of special functions of importance in physics. Where appropriate, the survey includes generating functions, Rodrigues formulas, the relevant differential equation, orthogonality conditions, and applications. The discussion covers Hermite functions (with applications to the quantum harmonic oscillator and to molecular vibrations), Laguerre functions (with application to the hydrogen atom), Chebyshev polynomials (with application to numerical analysis), hypergeometric and confluent hypergeometric functions, the dilogarithm (with application to electronic structure computations), and elliptic integrals.