Racah polynomials
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1: 18.26 Wilson Class: Continued
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18.26.4_2
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18.26.9
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18.26.10
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18.26.16
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►Koornwinder (2009) rescales and reparametrizes Racah polynomials and Wilson polynomials in such a way that they are continuous in their four parameters, provided that these parameters are nonnegative.
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2: 18.25 Wilson Class: Definitions
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►Table 18.25.1 lists the transformations of variable, orthogonality ranges, and parameter constraints that are needed in §18.2(i) for the Wilson polynomials
, continuous dual Hahn polynomials
, Racah polynomials
, and dual Hahn polynomials
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Table 18.25.1: Wilson class OP’s: transformations of variable, orthogonality ranges, and parameter constraints.
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OP | Orthogonality range for | Constraints | ||
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Racah | or or for further constraints see (18.25.1) | |||
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Further Constraints for Racah Polynomials
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18.25.10
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3: 18.28 Askey–Wilson Class
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►Both the Askey–Wilson polynomials and the -Racah polynomials can best be described as functions of (resp.
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§18.28(viii) -Racah Polynomials
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18.28.23
, , or ; .
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►These systems are the -Racah polynomials and its limit cases.
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18.28.34
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4: 18.1 Notation
5: 18.38 Mathematical Applications
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Coding Theory
►For applications of Krawtchouk polynomials and -Racah polynomials to coding theory see Bannai (1990, pp. 38–43), Leonard (1982), and Chihara (1987). … ►The symbol (34.4.3), with an alternative expression as a terminating balanced of unit argument, can be expressend in terms of Racah polynomials (18.26.3). The orthogonality relations (34.5.14) for the symbols can be rewritten in terms of orthogonality relations for Racah polynomials as given by (18.25.9)–(18.25.12). … …6: 16.4 Argument Unity
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►One example of such a three-term relation is the recurrence relation (18.26.16) for Racah polynomials.
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7: 18.21 Hahn Class: Interrelations
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8: Bibliography C
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Asymptotics of Racah coefficients and polynomials.
J. Phys. A 32 (3), pp. 537–553.
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