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11—20 of 344 matching pages
11: About the Project
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►These products resulted from the leadership of the Editors and Associate Editors pictured in Figure 1; the contributions of 29 authors, 10 validators, and 5 principal developers; and assistance from a large group of contributing developers, consultants, assistants and interns.
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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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12: 1.7 Inequalities
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►In this subsection and are positive constants.
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►Also and are constants that are not simultaneously zero.
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►Equality holds iff for all .
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13: 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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14: DLMF Project News
error generating summary15: Viewing DLMF Interactive 3D Graphics
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►Below we provide some notes and links to online material which might be helpful in viewing our visualizations, but please see our Disclaimer.
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16: Foreword
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►The online version, the NIST Digital
Library of Mathematical Functions (DLMF), presents the same technical information along with extensions and innovative interactive features consistent with the new medium.
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17: 3.12 Mathematical Constants
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►For access to online high-precision numerical values of mathematical constants see Sloane (2003).
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18: 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.
19: Bibliography L
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Some differential equations and associated integral equations.
Quart. J. Math. (Oxford) 5, pp. 81–97.
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Moment integrals of powers of Airy functions.
Z. Angew. Math. Phys. 44 (5), pp. 891–908.
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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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Theory of the fourth Painlevé equation.
Differ. Uravn. 3 (5), pp. 771–780 (Russian).
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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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20: Bibliography N
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Uniform asymptotic expansion for the incomplete beta function.
SIGMA Symmetry Integrability Geom. Methods Appl. 12, pp. 101, 5 pages.
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The resurgence properties of the incomplete gamma function, I.
Anal. Appl. (Singap.) 14 (5), pp. 631–677.
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Inequalities involving Bessel functions of the first kind.
JIPAM. J. Inequal. Pure Appl. Math. 5 (4), pp. Article 94, 4 pp. (electronic).
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The asymptotic behavior of the general real solution of the third Painlevé equation.
Dokl. Akad. Nauk SSSR 283 (5), pp. 1161–1165 (Russian).
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Diffraction Effects in Semiclassical Scattering.
Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.
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