Hilbert%20space
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21—30 of 144 matching pages
21: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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Methods of mathematical physics. Vol. I.
Interscience Publishers, Inc., New York, N.Y..
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22: 1.1 Special Notation
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real variables. | |
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the space of all Lebesgue–Stieltjes measurable functions on which are square integrable with respect to . | |
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the space of all -dimensional vectors. | |
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23: Errata
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Usability
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Section 1.14
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Chapters 8, 20, 36
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References
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Poor spacing in math was corrected in several chapters.
There have been extensive changes in the notation used for the integral transforms defined in §1.14. These changes are applied throughout the DLMF. The following table summarizes the changes.
Transform | New | Abbreviated | Old |
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Notation | Notation | Notation | |
Fourier | |||
Fourier Cosine | |||
Fourier Sine | |||
Laplace | |||
Mellin | |||
Hilbert | |||
Stieltjes |
Previously, for the Fourier, Fourier cosine and Fourier sine transforms, either temporary local notations were used or the Fourier integrals were written out explicitly.
24: 18.2 General Orthogonal Polynomials
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►A system of OP’s satisfying (18.2.1) and (18.2.5) is complete if each in the Hilbert space
can be approximated in Hilbert norm by finite sums .
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25: 8 Incomplete Gamma and Related
Functions
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26: 28 Mathieu Functions and Hill’s Equation
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27: 20.12 Mathematical Applications
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►The space of complex tori (that is, the set of complex numbers in which two of these numbers and are regarded as equivalent if there exist integers such that ) is mapped into the projective space
via the identification .
…This ability to uniformize multiply-connected spaces (manifolds), or multi-sheeted functions of a complex variable (Riemann (1899), Rauch and Lebowitz (1973), Siegel (1988)) has led to applications in string theory (Green et al. (1988a, b), Krichever and Novikov (1989)), and also in statistical mechanics (Baxter (1982)).
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28: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
29: 23 Weierstrass Elliptic and Modular
Functions
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30: Bibliography K
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Separation of Variables for Riemannian Spaces of Constant Curvature.
Longman Scientific & Technical, Harlow.
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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