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== Special Functions == * Gamma Function (Ξ) ** Generalization of the factorial function to complex numbers. *** Analyzing divergent series, statistical distributions. * Beta Function (B) ** Function defined by an integral. *** Statistical distributions, probability density functions. * Riemann Zeta Function (ΞΆ) ** Analytic function that generalizes the sum of the infinite series. *** Analyzing prime numbers, number theory. * Bessel Functions (J, Y, I, K) ** Solutions to Bessel's differential equation. *** Modeling oscillations, heat conduction. * Legendre Polynomials (P) ** Orthogonal polynomials that arise in the solution of Laplace's equation. *** Quantum mechanics, celestial mechanics. * Hermite Polynomials (H) ** Orthogonal polynomials that arise in the solution of the quantum harmonic oscillator. *** Quantum mechanics, statistical mechanics. * Laguerre Polynomials (L) ** Orthogonal polynomials that arise in the solution of the quantum hydrogen atom. *** Quantum mechanics, atomic physics.
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