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… ►For properties see Virchenko and Fedotova (2001) and Braaksma and Meulenbeld (1967). … ►For inhomogeneous versions of the associated Legendre equation, and properties of their solutions, see Babister (1967, pp. 252–264).
… ►He was also editor of The Kowalevski Property, CRM Proceedings and Lecture Notes 32, published by the American Mathematical Society in 2002. …
§32.16 Physical Applications…
… ►Their similarity solutions lead to special ODEs which have the Painlevé property; i. …ODEs with the Painlevé property contain the well-known Painlevé equations which are special second order scalar equations; their solutions are often called Painlevé transcendents. …
§28.12 Definitions and Basic Properties… ►
28.12.2… ►They have the following pseudoperiodic and orthogonality properties: … ►
§28.12(iii) Functions , , when…
Table 18.3.1: Orthogonality properties for classical OP’s: intervals, weight functions, normalizations, leading coefficients, and parameter constraints.
… ►In addition to the orthogonal property given by Table 18.3.1, the Chebyshev polynomials , , are orthogonal on the discrete point set comprising the zeros , of : … ►For proofs of these results and for similar properties of the Chebyshev polynomials of the second, third, and fourth kinds see Mason and Handscomb (2003, §4.6). ►For another version of the discrete orthogonality property of the polynomials see (3.11.9). … ►In consequence, additional properties are included in Chapter 14.