# relation to minimax polynomials

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##### 11: 18.36 Miscellaneous Polynomials
###### §18.36 Miscellaneous Polynomials
These are OP’s on the interval $(-1,1)$ with respect to an orthogonality measure obtained by adding constant multiples of “Dirac delta weights” at $-1$ and $1$ to the weight function for the Jacobi polynomials. … These are polynomials in one variable that are orthogonal with respect to a number of different measures. They are related to Hermite–Padé approximation and can be used for proofs of irrationality or transcendence of interesting numbers. … These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. …
##### 13: 19.10 Relations to Other Functions
###### §19.10(i) Theta and Elliptic Functions
For relations of Legendre’s integrals to theta functions, Jacobian functions, and Weierstrass functions, see §§20.9(i), 22.15(ii), and 23.6(iv), respectively. …
###### §19.10(ii) Elementary Functions
For relations to the Gudermannian function $\operatorname{gd}\left(x\right)$ and its inverse ${\operatorname{gd}^{-1}}\left(x\right)$4.23(viii)), see (19.6.8) and …
##### 14: 25.17 Physical Applications
###### §25.17 Physical Applications
This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian. … Quantum field theory often encounters formally divergent sums that need to be evaluated by a process of regularization: for example, the energy of the electromagnetic vacuum in a confined space (Casimir–Polder effect). It has been found possible to perform such regularizations by equating the divergent sums to zeta functions and associated functions (Elizalde (1995)).
##### 15: 16.25 Methods of Computation
Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations. They are similar to those described for confluent hypergeometric functions, and hypergeometric functions in §§13.29 and 15.19. There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations). …Instead a boundary-value problem needs to be formulated and solved. …
##### 18: 16.24 Physical Applications
For an extension to two-loop integrals see Moch et al. (2002).
###### §16.24(iii) $\mathit{3j}$, $\mathit{6j}$, and $\mathit{9j}$ Symbols
The coefficients of transformations between different coupling schemes of three angular momenta are related to the Wigner $\mathit{6j}$ symbols. …
##### 20: Mourad E. H. Ismail
Ismail has published numerous papers on special functions, orthogonal polynomials, approximation theory, combinatorics, asymptotics, and related topics. His well-known book Classical and Quantum Orthogonal Polynomials in One Variable was published by Cambridge University Press in 2005 and reprinted with corrections in paperback in Ismail (2009). …  190, American Mathematical Society, 1995; Special Functions, $q$-Series and Related Topics (with D. … Garvan), Kluwer Academic Publishers, 2001; and Theory and Applications of Special Functions: A volume dedicated to Mizan Rahman (with E. …