1 The Askey Scheme of Orthogonal Polynomials -- 2.1 Markov Processes -- 3 Birth and Death Processes, Random Walks, and Orthogonal Polynomials -- 4 Sheffer Systems -- 5 Orthogonal Polynomials in Stochastic Integration Theory -- Stein Approximation and Orthogonal Polynomials -- Conclusion -- A Distributions -- B Tables of Classical Orthogonal Polynomials -- B.1 Hermite Polynomials and the Normal Distribution -- B.2 Scaled Hermite Polynomials and the Standard Normal Distribution -- B.3 Hermite Polynomials with Parameter and the Normal Distribution -- B.4 Charlier Polynomials and the Poisson Distribution -- B.5 Laguerre Polynomials and the Gamma Distribution -- B.6 Meixner Polynomials and the Pascal Distribution -- B.7 Krawtchouk Polynomials and the Binomial Distribution -- B.8 Jacobi Polynomials and the Beta Kernel -- B.9 Hahn Polynomials and the Hypergeometric Distribution -- C Table of Duality Relations Between Classical Orthogonal Polynomials -- D Tables of Sheffer Systems -- D.1 Sheffer Polynomials and Their Generating Functions -- D.2 Sheffer Polynomials and Their Associated Distributions -- D.3 Martingale Relations with Sheffer Polynomials -- E Tables of Limit Relations Between Orthogonal Polynomials in the Askey Scheme -- References

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