# relation to minimax polynomials

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##### 1: 35.4 Partitions and Zonal Polynomials
###### §35.4 Partitions and Zonal Polynomials
For any partition $\kappa$, the zonal polynomial $Z_{\kappa}:\boldsymbol{\mathcal{S}}\to\mathbb{R}$ is defined by the properties …
##### 2: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
###### §31.5 Solutions Analytic at Three Singularities: Heun Polynomials
is a polynomial of degree $n$, and hence a solution of (31.2.1) that is analytic at all three finite singularities $0,1,a$. These solutions are the Heun polynomials. …
##### 3: 24.1 Special Notation
###### Bernoulli Numbers and Polynomials
The origin of the notation $B_{n}$, $B_{n}\left(x\right)$, is not clear. …
###### Euler Numbers and Polynomials
The notations $E_{n}$, $E_{n}\left(x\right)$, as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …
##### 4: 18.3 Definitions
###### §18.3 Definitions
For explicit power series coefficients up to $n=12$ for these polynomials and for coefficients up to $n=6$ for Jacobi and ultraspherical polynomials see Abramowitz and Stegun (1964, pp. 793–801). … In addition to the orthogonal property given by Table 18.3.1, the Chebyshev polynomials $T_{n}\left(x\right)$, $n=0,1,\dots,N$, are orthogonal on the discrete point set comprising the zeros $x_{N+1,n},n=1,2,\dots,N+1$, of $T_{N+1}\left(x\right)$: … It is also related to a discrete Fourier-cosine transform, see Britanak et al. (2007). …
##### 5: 3.11 Approximation Techniques
###### §3.11(i) MinimaxPolynomial Approximations
For examples of minimax polynomial approximations to elementary and special functions see Hart et al. (1968). … They satisfy the recurrence relationThe theory of polynomial minimax approximation given in §3.11(i) can be extended to the case when $p_{n}(x)$ is replaced by a rational function $R_{k,\ell}(x)$. …
##### 6: 16.7 Relations to Other Functions
###### §16.7 Relationsto Other Functions
For orthogonal polynomials see Chapter 18. …
##### 7: 18.38 Mathematical Applications
The Askey–Gasper inequalityThe orthogonality relations in §34.3(iv) for the $3j$ symbols can be rewritten in terms of orthogonality relations for Hahn or dual Hahn polynomials as given by §§18.2(i), 18.2(iii) and Table 18.19.1 or by §18.25(iii), respectively. … … The orthogonality relations (34.5.14) for the $6j$ symbols can be rewritten in terms of orthogonality relations for Racah polynomials as given by (18.25.9)–(18.25.12). … …
##### 8: 6.11 Relations to Other Functions
###### Confluent Hypergeometric Function
6.11.3 $\mathrm{g}\left(z\right)+i\mathrm{f}\left(z\right)=U\left(1,1,-iz\right).$