mathematical%20definitions

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1: Foreword

… ►In 1964 the National Institute of Standards and Technology published the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by Milton Abramowitz and Irene A. … ►Certainly, advances in applied mathematics have continued unabated. …The new printed volume, the NIST Handbook of Mathematical Functions, serves a similar function as the original A&S, though it is heavily updated and extended. …The DLMF may well serve as a model for the effective presentation of highly mathematical reference material on the Web. … ►November 20, 2009 …

2: Errata

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Pochhammer and $q$-Pochhammer symbols in several equations now correctly link to their definitions.

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Linkage of mathematical symbols to their definitions were corrected or improved.

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In many cases, the links from mathematical symbols to their definitions were corrected or improved. These links were also enhanced with ‘tooltip’ feedback, where supported by the user’s browser.

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Several new equations have been added. See (8.17.24), (20.7.34), §20.11(v), (26.12.27), (36.2.28), and (36.2.29).

… ►The Handbook of Mathematical Functions was published, and the Digital Library of Mathematical Functions was released.

3: Bibliography R

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On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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External Links:

ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

Encodings:

BibTeX

… ►

Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness. Academic Press, New York.

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External Links:

ISBN 978-0-12-585002-5, MathReview Entry

Referenced by:

§1.18(x).

Encodings:

BibTeX

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Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators. Academic Press, New York.

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External Links:

ISBN 0-12-585004-2(vol.4), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

Encodings:

BibTeX

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Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory. Academic Press, New York.

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External Links:

ISBN 0-12-585003-4 (vol.3), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

Encodings:

BibTeX

… ►

Principles of Mathematical Analysis. 3rd edition, McGraw-Hill Book Co., New York.

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Notes:

International Series in Pure and Applied Mathematics

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.4(iii).

Encodings:

BibTeX

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4: 14.30 Spherical and Spheroidal Harmonics

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§14.30(i) Definitions

… ►Sometimes $Y_{l,m}(\theta ,\varphi )$ is denoted by ${\mathrm{i}}^{-l}{𝔇}_{lm}(\theta ,\varphi )$; also the definition of $Y_{l,m}(\theta ,\varphi )$ can differ from (14.30.1), for example, by inclusion of a factor ${(-1)}^m$. … ►Most mathematical properties of $Y_{l,m}(\theta ,\varphi )$ can be derived directly from (14.30.1) and the properties of the Ferrers function of the first kind given earlier in this chapter. … ►

14.30.4

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Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $Y_{l,m}(\theta ,\varphi )$: spherical harmonic, $m$: integer and $l$: nonnegative integer

Referenced by:

§14.30(ii), Erratum (V1.0.25) for Section 14.30

Permalink:

http://dlmf.nist.gov/14.30.E4

Encodings:

pMML, png, TeX

Correction (effective with 1.0.25):

Previously this equation was only given for $m\ge 0$. In this update we have extended the definition of spherical harmonics to include negative integer values such that $|m|\le l$. Hence in the second part of this equation, we have replaced $m$ with $|m|$.

Suggested 2019-10-15 by Ching-Li Chai

See also:

Annotations for §14.30(ii), §14.30(ii), §14.30 and Ch.14

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