Abstract
In this chapter, we address several of the many applications of the classical orthogonal polynomial sequences. These applications include first-order differential equations that characterize linear generating functions, additional first-order differential equations, second-order differential equations (with applications to quantum mechanics), difference equations and numerical integration (Gaussian Quadrature). We first develop each of these applications in a general context and then cover examples using specific Sheffer Sequences, i.e. the Laguerre, Hermite, Charlier, Meixner, Meixner–Pollaczek, and Krawtchouk polynomials.
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© 2013 Daniel J. Galiffa
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Galiffa, D.J. (2013). Some Applications of the Sheffer A-Type 0 Orthogonal Polynomial Sequences. In: On the Higher-Order Sheffer Orthogonal Polynomial Sequences. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5969-9_2
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DOI: https://doi.org/10.1007/978-1-4614-5969-9_2
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