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The Mathematica GuideBook for Symbolics pp 802–977Cite as

Classical Orthogonal Polynomials

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Abstract

In this chapter, we discuss the classical orthogonal polynomials. Our main purpose is to provide formulas that uniquely define the polynomials (including normalization factors) and to demonstrate some of Mathematica’s integration, differentiation, and series expansion capabilities. Further, we will make use of graphics to visualize the orthogonal polynomials in a variety of ways. In this chapter, we sometimes use the word “check” not in the sense of a mathematical proof, but rather in the sense of checking formulas by means of special cases and computational examples. (For the use of Mathematica as a theorem prover, see [145], [330].) Occasionally we will encounter special functions (especially the Gamma function and the Gauss hypergeometric function) in this chapter when carrying out integrals involving orthogonal polynomials. We will discuss these functions in the next chapter.

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(2006). Classical Orthogonal Polynomials. In: The Mathematica GuideBook for Symbolics. Springer, New York, NY. https://doi.org/10.1007/0-387-28815-5_2

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