…
►
►‘✓’
indicates that a software package implements the functions in a section; ‘
a’
indicates available functionality through optional or add-on packages;
an empty space
indicates no known support.
…
►
Software Associated with Books.
An increasing number of published books have
included digital media containing software described in the book. Often, the
collection of software covers a fairly broad area. Such software is typically
developed by the book author. While it is not professionally packaged,
it often provides a useful tool for readers to experiment with the concepts
discussed in the book. The software itself is typically not formally supported
by its authors.
►
Commercial Software.
Such software ranges from a collection of reusable software
parts (e.g., a library) to fully functional interactive computing environments
with an associated computing language. Such software is usually professionally
developed, tested, and maintained to high standards. It is available for purchase,
often with accompanying updates and consulting support.
…
…
►
►Unless otherwise noted, primes
indicate derivatives with respect to the argument.
…
…
►He is both
an Associate Editor for Chemistry and a Senior Associate Editor for the DLMF.
…
►This is closely connected with his interests in classical dynamical “chaos,”
an area where he coauthored a book,
Chaos in atomic physics with Reinhold Blümel.
…
►
…
►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters
20,
22, and
23.
…
►Walker’s books are
An Introduction to Complex Analysis, published by Hilger in 1974,
The Theory of Fourier Series and Integrals, published by Wiley in 1986,
Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and
Examples and Theorems in Analysis, published by Springer in 2004.
…
►
…
►In November 2015, Walker was named
an Associate Editor for his chapters.
…
►
An Introductory Remark
…
►In what follows the radial and spherical radial eigenfunctions corresponding to (
18.39.27) are found in four
different notations, with identical eigenvalues, all of which appear in the current and past mathematical and theoretical physics and chemistry literatures, regarding this central problem.
…
►This
indicates that the Laguerre polynomials appearing in (
18.39.29) are not classical OP’s, and in fact, even though infinite in number for fixed
, do not form a complete set.
…
►see
Bethe and Salpeter (1957, p. 13),
Pauling and Wilson (1985, pp. 130, 131); and noting that this
differs from the Rodrigues formula of (
18.5.5) for the Laguerre OP’s, in the omission of
an
in the denominator.
…
►Derivations of (
18.39.42) appear in
Bethe and Salpeter (1957, pp. 12–20), and
Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (
18.39.36), and is also the notation of
Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry.
…
…
►As of September
20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter
25 Zeta and Related Functions.
…