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1: 34.6 Definition: $\mathit{9}j$ Symbol

§34.6 Definition: $\mathit{9}j$ Symbol

►The $\mathit{9}j$ symbol may be defined either in terms of $\mathit{3}j$ symbols or equivalently in terms of $\mathit{6}j$ symbols: ►

34.6.1

ⓘ

Defines:

: $\mathit{9}j$ symbol

Symbols:

: $\mathit{3}j$ symbol, $j,j_r$: non-negative integers or non-negative integers plus one half., $r$: nonnegative integer and $s$: integer

Permalink:

http://dlmf.nist.gov/34.6.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §34.6 and Ch.34

►

34.6.2

ⓘ

Symbols:

: $\mathit{9}j$ symbol, : $\mathit{6}j$ symbol and $j,j_r$: non-negative integers or non-negative integers plus one half.

Referenced by:

§34.13

Permalink:

http://dlmf.nist.gov/34.6.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §34.6 and Ch.34

►The $\mathit{9}j$ symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments. …

2: 26.9 Integer Partitions: Restricted Number and Part Size

… ► $p_k\left(n\right)$ denotes the number of partitions of $n$ into at most $k$ parts. See Table 26.9.1. … ►Conjugation establishes a one-to-one correspondence between partitions of $n$ into at most $k$ parts and partitions of $n$ into parts with largest part less than or equal to $k$. … ► $p_k(\le m,n)$ is the number of partitions of $n$ into at most $k$ parts, each less than or equal to $m$. …

3: Richard B. Paris

… ► 2022) was Reader in Mathematics at the University of Abertay Dundee, U. …He also had an honorary appointment at the University of St. …Previously, he was employed by Euratom at the French Atomic Energy Commission at Fontenay-aux-Roses and Cadarache. … ►

8 Incomplete Gamma and Related Functions

…

4: DLMF Project News

error generating summary

5: Diego Dominici

… … ► 2023) studied Pure Mathematics at the Universidad de Buenos Aires, Argentina, and did his Ph. …in Applied Mathematics at the University of Illinois at Chicago (UIC) under the direction of Charles Knessl and Noemí Irene Wolanski. Diego was a Full Professor at the State University of New York at New Paltz where he was Department Chair for many years. Since May 2023 Diego worked as a senior researcher at the Research Institute for Symbolic Computation at Johannes Kepler Universität, Linz, Austria. …

6: 4.3 Graphics

… ►

►►

Figure 4.3.1: $\ln x$ and ${\mathrm{e}}^x$. Parallel tangent lines at $(1,0)$ and $(0,1)$ make evident the mirror symmetry across the line $y=x$, demonstrating the inverse relationship between the two functions. Magnify

… ►Lines parallel to the real axis in the $z$-plane map onto rays in the $w$-plane, and lines parallel to the imaginary axis in the $z$-plane map onto circles centered at the origin in the $w$-plane. … ►

►

… ►

►►

	A	B	C	$\overline{\mathrm{C}}$	D	$\overline{\mathrm{D}}$	E	$\overline{\mathrm{E}}$	F
…

►

Figure 4.3.2: Conformal mapping of exponential and logarithm. … Magnify

…

7: Tom M. Apostol

… ► 2016) was Professor Emeritus in the Department of Mathematics at the California Institute of Technology (Caltech), Pasadena, California, until his death on May 8, 2016. … ►In 1950, he arrived at Caltech as an assistant professor; he was named associate professor in 1956, professor in 1962, and professor emeritus in 1992. ►He was a visiting professor at the University of Patras in Greece in 1978, and was elected a Corresponding Member of the Academy of Athens in 2001 (where he delivered his inaugural lecture in Greek). … ►The videos captured first-place honors at a dozen international video festivals, and have been translated into Hebrew, Portuguese, French, and Spanish. …

8: Bille C. Carlson

… ►Department of Energy) at Iowa State University, Ames, Iowa, until his death on August 16, 2013. … ►He began studies at Harvard College, but joined the U. …Navy after the onset of World War II and worked on the island of Guam with radar, which was novel at the time. …After four years in the Physics Department at Princeton, he went to the Ames Laboratory and Iowa State University in 1954, where he was a Professor in the Physics and Mathematics Departments. … ►In his paper Lauricella’s hypergeometric function $F_D$ (1963), he defined the $R$-function, a multivariate hypergeometric function that is homogeneous in its variables, each variable being paired with a parameter. …

9: 26.10 Integer Partitions: Other Restrictions

… ► $p_m(𝒟,n)$ denotes the number of partitions of $n$ into at most $m$ distinct parts. $p(𝒟k,n)$ denotes the number of partitions of $n$ into parts with difference at least $k$. $p({𝒟}^{\prime }3,n)$ denotes the number of partitions of $n$ into parts with difference at least 3, except that multiples of 3 must differ by at least 6. … ►Note that $p({𝒟}^{\prime }3,n)\le p(𝒟3,n)$, with strict inequality for $n\ge 9$. … ►The quantity $A_k(n)$ is real-valued. …

10: Leonard C. Maximon

… ► 2020) was a Research Professor of Physics in the Department of Physics at The George Washington University. He had been an Assistant Professor in the Graduate Division of Applied Mathematics at Brown University, a Visiting Professor at the Norwegian Technical University in Trondheim, Norway, and a Physicist at the Center for Radiation Research at the National Bureau of Standards. … ►

34 3j, 6j, 9j Symbols

…