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11: Notices
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Index of Selected Software Within the DLMF Chapters
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Within each of the DLMF chapters themselves we will provide a list of research software for the functions discussed in that chapter. The purpose of these listings is to provide references to the research literature on the engineering of software for special functions. To qualify for listing, the development of the software must have been the subject of a research paper published in the peer-reviewed literature. If such software is available online for free download we will provide a link to the software.
In general, we will not index other software within DLMF chapters unless the software is unique in some way, such as being the only known software for computing a particular function.
12: Bibliography U
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Mathematics of Computation Unpublished Mathematical Tables Collection.
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13: About the Project
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►They were selected as recognized leaders in the research communities interested in the mathematics and applications of special functions and orthogonal polynomials; in the presentation of mathematics reference information online and in handbooks; and in the presentation of mathematics on the web.
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14: Bibliography M
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Hypergeometric Functions.
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Maplesoft.
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On the evaluation of the integral over the product of two spherical Bessel functions.
J. Math. Phys. 32 (3), pp. 642–648.
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Derivatives of the Hurwitz zeta function for rational arguments.
J. Comput. Appl. Math. 100 (2), pp. 201–206.
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Zeros of first derivatives of Bessel functions of the first kind, , ,
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J. Res. Nat. Bur. Standards Sect. B 67B (3), pp. 181–183.
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15: Bibliography L
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Numerical Evaluation of Special Functions.
In Mathematics of Computation 1943–1993: A Half-Century of
Computational Mathematics (Vancouver, BC, 1993),
Proc. Sympos. Appl. Math., Vol. 48, pp. 79–125.
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Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray.
Math. Comp. 17 (84), pp. 395–404.
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16: 18.39 Applications in the Physical Sciences
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►where is a spatial coordinate, the mass of the particle with potential energy , is the reduced Planck’s constant, and a finite or infinite interval.
►Here the term represents the quantum kinetic energy of a single particle of mass , and its potential energy.
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►and , has eigenfunctions
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►The eigenfunctions of are the spherical harmonics with eigenvalues , each with degeneracy as .
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►, , Mohr and Taylor (2005, Table XXX, p. 71), where the relationship of to SI units is spelled out.
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17: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►A complex linear vector space is called an inner product space if an inner product
is defined for all with the properties: (i) is complex linear in ; (ii) ; (iii) ; (iv) if then .
…Two elements and in are orthogonal if .
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►Functions for which are identified with each other.
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►, , for .
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►The adjoint of does satisfy where .
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18: 1.2 Elementary Algebra
19: Karl Dilcher
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►Over the years he authored or coauthored numerous papers on Bernoulli numbers and related topics, and he maintains a large on-line bibliography on the subject.
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