Abstract
A function that often takes place in the study of special functions is the Gamma function, which is needed particularly on Bessel function description. Bessel functions arise in many problems possessing cylindrical symmetry, in the study of the wave and heat equations and in the study of the Kepler problem of describing planetary motion, and provide another orthogonal set of basis functions. The Legendre polynomials are one of a set of classical orthogonal polynomials, which satisfy a second-order linear ODE, so-called Legendre ODE occurring naturally in the solution of initial value problems having spherical symmetry.
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