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11: 16.4 Argument Unity

… ► … ► … ► … ►See also Lewanowicz (1985) (with corrections in Lewanowicz (1987)) for further examples of recurrence relations. …

12: 15.17 Mathematical Applications

… ►Harmonic analysis can be developed for the Jacobi transform either as a generalization of the Fourier-cosine transform (§1.14(ii)) or as a specialization of a group Fourier transform. For further information see Koornwinder (1984a). …

13: 4.12 Generalized Logarithms and Exponentials

§4.12 Generalized Logarithms and Exponentials

►A generalized exponential function $\varphi (x)$ satisfies the equations …Its inverse $\psi (x)$ is called a generalized logarithm. … ►For further information, see Clenshaw et al. (1986). …For analytic generalized logarithms, see Kneser (1950).

14: 18.40 Methods of Computation

… ►For applications in which the OP’s appear only as terms in series expansions (compare §18.18(i)) the need to compute them can be avoided altogether by use instead of Clenshaw’s algorithm (§3.11(ii)) and its straightforward generalization to OP’s other than Chebyshev. For further information see Clenshaw (1955), Gautschi (2004, §§2.1, 8.1), and Mason and Handscomb (2003, §2.4). … ►Further, exponential convergence in $N$, via the Derivative Rule, rather than the power-law convergence of the histogram methods, is found for the inversion of Gegenbauer, Attractive, as well as Repulsive, Coulomb–Pollaczek, and Hermite weights and zeros to approximate $w(x)$ for these OP systems on $x\in [-1,1]$ and $(-\mathrm{\infty },\mathrm{\infty })$ respectively, Reinhardt (2018), and Reinhardt (2021b), Reinhardt (2021a). …

15: 20 Theta Functions

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16: 18.27 $q$-Hahn Class

… ►The generic (top level) cases are the $q$-Hahn polynomials and the big $q$-Jacobi polynomials, each of which depends on three further parameters. …

17: 18.38 Mathematical Applications

… ►This process has been generalized to spectral methods for solving partial differential equations. For further information see Mason and Handscomb (2003, Chapters 10 and 11), Gottlieb and Orszag (1977, pp. 7–19), and Guo (1998, pp. 120–151). … ►The Askey–Gasper inequality … ►Define a further operator $K_2$ by …A further operator, the so-called Casimir operator …

18: 23.20 Mathematical Applications

… ►For further information, including the application of (23.20.7) to the solution of the general quintic equation, see Borwein and Borwein (1987, Chapter 4). …

19: 16.7 Relations to Other Functions

§16.7 Relations to Other Functions

… ►Further representations of special functions in terms of ${}_p{}^{}F_q^{}$ functions are given in Luke (1969a, §§6.2–6.3), and an extensive list of ${}_{q+1}{}^{}F_q^{}$ functions with rational numbers as parameters is given in Krupnikov and Kölbig (1997).

20: 10.43 Integrals

… ►For further properties of the Bickley function, including asymptotic expansions and generalizations, see Amos (1983c, 1989) and Luke (1962, Chapter 8). …