Abstract
The theory of Hilbert spaces we dealt with in Chap. 4 can be used to construct a number of polynomial functions that are orthonormal and complete in the sense of the Lp space. In this chapter we present three important approaches for the construction of orthonormal polynomials, based, respectively, on the Weierstrass theorem (Sect. 5.1.1), the Rodrigues formula (Sect. 5.2.1), and generating functions (Sect. 5.2.7). We shall find that various orthonormal polynomials relevant to mathematical physics can be effectively classified by adopting these methods.
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© 2009 Springer-Verlag Berlin Heidelberg
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Shima, H., Nakayama, T. (2009). Orthonormal Polynomials. In: Higher Mathematics for Physics and Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b138494_5
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DOI: https://doi.org/10.1007/b138494_5
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-540-87864-3
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