specialization

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21: Hans Volkmer

… ►Schäfke in 1979 on a topic in special functions. … ►Volkmer has published numerous papers on special functions, spectral theory, differential equations, and mathematical statistics. …

22: About MathML

… ►

Special fonts for MathML

►Since the display of mathematics involves many special symbols not often seen in plain text, a MathML renderer generally needs special fonts. …

… ►That 1046-page tome proved to be an invaluable reference for the many scientists and engineers who use the special functions of applied mathematics in their day-to-day work, so much so that it became the most widely distributed and most highly cited NIST publication in the first 100 years of the institution’s existence. ²² 2 D. R. Lide (ed.), A Century of Excellence in Measurement, Standards, and Technology, CRC Press, 2001. The success of the original handbook, widely referred to as “Abramowitz and Stegun” (“A&S”), derived not only from the fact that it provided critically useful scientific data in a highly accessible format, but also because it served to standardize definitions and notations for special functions. … ►However, we have also seen the birth of a new age of computing technology, which has not only changed how we utilize special functions, but also how we communicate technical information. …

24: 12.1 Special Notation

§12.1 Special Notation

►(For other notation see Notation for the Special Functions.) …

25: 25.1 Special Notation

§25.1 Special Notation

►(For other notation see Notation for the Special Functions.) …

26: 3 Numerical Methods

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27: 4.31 Special Values and Limits

§4.31 Special Values and Limits

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28: 15.17 Mathematical Applications

… ► … ►For special values of

\alpha

and

\beta

there are many group-theoretic interpretations. …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. …

29: 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).

30: 18.6 Symmetry, Special Values, and Limits to Monomials

§18.6 Symmetry, Special Values, and Limits to Monomials

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§18.6(i) Symmetry and Special Values

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Table 18.6.1: Classical OP’s: symmetry and special values.

► ►►

$p_{n}(x)$	$p_{n}(-x)$	$p_{n}(1)$	$p_{2n}(0)$	$p_{2n+1}^{\prime}(0)$
…

► …