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1: 34.4 Definition: $\mathit{6}j$ Symbol

§34.4 Definition: $\mathit{6}j$ Symbol

►The $\mathit{6}j$ symbol is defined by the following double sum of products of $\mathit{3}j$ symbols: … ►The $\mathit{6}j$ symbol can be expressed as the finite sum … ►where ${}_4{}^{}F_3^{}$ is defined as in §16.2. ►For alternative expressions for the $\mathit{6}j$ symbol, written either as a finite sum or as other terminating generalized hypergeometric series ${}_4{}^{}F_3^{}$ of unit argument, see Varshalovich et al. (1988, §§9.2.1, 9.2.3).

2: DLMF Project News

error generating summary

3: Publications

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From 2D to 3D: Numerical Grid Generation and the Visualization of Complex Surfaces, Proceedings of the 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler, British Columbia, Canada, September 25-28, 2000.

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Dissemination of 3D Visualizations of Complex Function Data for the NIST Digital Library of Mathematical Functions, CODATA Data Science Journal 6 (2007), pp. S146–S154.

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A Special Functions Handbook for the Digital Age, Notices of the American Mathematical Society 58, 7 (2011), pp. 905–911.

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4: Foreword

… ►However, we have also seen the birth of a new age of computing technology, which has not only changed how we utilize special functions, but also how we communicate technical information. …

5: Frank W. J. Olver

… ►Having witnessed the birth of the computer age firsthand (as a colleague of Alan Turing at NPL, for example), Olver is also well known for his contributions to the development and analysis of numerical methods for computing special functions. … ►He continued his editing work until the time of his death on April 22, 2013 at age 88.

6: 6 Exponential, Logarithmic, Sine, and
Cosine Integrals

Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals

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7: 34.12 Physical Applications

§34.12 Physical Applications

►The angular momentum coupling coefficients ($\mathit{3}j$, $\mathit{6}j$, and $\mathit{9}j$ symbols) are essential in the fields of nuclear, atomic, and molecular physics. …$\mathit{3}j,\mathit{6}j$, and $\mathit{9}j$ symbols are also found in multipole expansions of solutions of the Laplace and Helmholtz equations; see Carlson and Rushbrooke (1950) and Judd (1976).

8: 34.14 Tables

§34.14 Tables

►Tables of exact values of the squares of the $\mathit{3}j$ and $\mathit{6}j$ symbols in which all parameters are $\le 8$ are given in Rotenberg et al. (1959), together with a bibliography of earlier tables of $\mathit{3}j,\mathit{6}j$, and $\mathit{9}j$ symbols on pp. … ► 11-12; for $\mathit{6}j$ symbols on pp. … ►Biedenharn and Louck (1981) give tables of algebraic expressions for Clebsch–Gordan coefficients and $\mathit{6}j$ symbols, together with a bibliography of tables produced prior to 1975. … 270–289; similar tables for the $\mathit{6}j$ symbols are given on pp. …

9: 34 3j, 6j, 9j Symbols

Chapter 34 $\mathit{3}j,\mathit{6}j,\mathit{9}j$ Symbols

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10: 23 Weierstrass Elliptic and Modular
Functions

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