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1: Mourad E. H. Ismail
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). …
2: 21.8 Abelian Functions
In consequence, Abelian functions are generalizations of elliptic functions (§23.2(iii)) to more than one complex variable. …
3: Bibliography I
  • M. E. H. Ismail (2005) Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
  • M. E. H. Ismail (2009) Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
  • 4: 1.4 Calculus of One Variable
    §1.4 Calculus of One Variable
    1.4.1 f ( c + ) lim x c + f ( x ) = f ( c ) ,
    §1.4(vi) Taylor’s Theorem for Real Variables
    See accompanying text
    Figure 1.4.2: Convex function f ( x ) . … Magnify
    5: 18.38 Mathematical Applications
    Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions
    This gives also new structures and results in the one-variable case, but the obtained nonsymmetric special functions can now usually be written as a linear combination of two known special functions. In the one-variable case the Dunkl operator eigenvalue equation … For the one-variable q -case see Noumi and Stokman (2004), Koornwinder (2007a, §§3,4), Koornwinder and Bouzeffour (2011, §§4,5) and Terwilliger (2013). …
    6: 31.16 Mathematical Applications
    By specifying either θ or ϕ in (31.16.1) and (31.16.2) we obtain expansions in terms of one variable. …
    7: 8.27 Approximations
  • Luke (1975, §4.3) gives Padé approximation methods, combined with a detailed analysis of the error terms, valid for real and complex variables except on the negative real z -axis. See also Temme (1994b, §3).

  • 8: 18.22 Hahn Class: Recurrence Relations and Differences
    §18.22(ii) Difference Equations in x
    9: 18.37 Classical OP’s in Two or More Variables
    Orthogonal polynomials associated with root systems are certain systems of trigonometric polynomials in several variables, symmetric under a certain finite group (Weyl group), and orthogonal on a torus. In one variable they are essentially ultraspherical, Jacobi, continuous q -ultraspherical, or Askey–Wilson polynomials. …
    10: 18.36 Miscellaneous Polynomials
    These are polynomials in one variable that are orthogonal with respect to a number of different measures. …