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1: 34.6 Definition: 9 j Symbol
§34.6 Definition: 9 j Symbol
The 9 j symbol may be defined either in terms of 3 j symbols or equivalently in terms of 6 j symbols:
34.6.1 { j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33 } = all  m r s ( j 11 j 12 j 13 m 11 m 12 m 13 ) ( j 21 j 22 j 23 m 21 m 22 m 23 ) ( j 31 j 32 j 33 m 31 m 32 m 33 ) ( j 11 j 21 j 31 m 11 m 21 m 31 ) ( j 12 j 22 j 32 m 12 m 22 m 32 ) ( j 13 j 23 j 33 m 13 m 23 m 33 ) ,
34.6.2 { j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33 } = j ( 1 ) 2 j ( 2 j + 1 ) { j 11 j 21 j 31 j 32 j 33 j } { j 12 j 22 j 32 j 21 j j 23 } { j 13 j 23 j 33 j j 11 j 12 } .
The 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: DLMF Project News
error generating summary
3: 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.
    4: Publications
  • B. R. Miller and A. Youssef (2003) Technical Aspects of the Digital Library of Mathematical Functions, Annals of Mathematics and Artificial Intelligence—Special Issue on Mathematical Knowledge Management, Vol. 38, Nos. 1–3, pp. 121–136. PDF
  • R. Boisvert, C. W. Clark, D. Lozier and F. Olver (2011) A Special Functions Handbook for the Digital Age, Notices of the American Mathematical Society 58, 7 (2011), pp. 905–911. PDF
  • 5: 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. …
    6: 34.12 Physical Applications
    §34.12 Physical Applications
    The angular momentum coupling coefficients ( 3 j , 6 j , and 9 j symbols) are essential in the fields of nuclear, atomic, and molecular physics. … 3 j , 6 j , and 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).
    7: 9 Airy and Related Functions
    Chapter 9 Airy and Related Functions
    8: 34 3j, 6j, 9j Symbols
    Chapter 34 3 j , 6 j , 9 j Symbols
    9: 34.14 Tables
    §34.14 Tables
    Tables of exact values of the squares of the 3 j and 6 j symbols in which all parameters are 8 are given in Rotenberg et al. (1959), together with a bibliography of earlier tables of 3 j , 6 j , and 9 j symbols on pp. … Some selected 9 j symbols are also given. … 16-17; for 9 j symbols on p. …  310–332, and for the 9 j symbols on pp. …
    10: 16.26 Approximations
    For discussions of the approximation of generalized hypergeometric functions and the Meijer G -function in terms of polynomials, rational functions, and Chebyshev polynomials see Luke (1975, §§5.12 - 5.13) and Luke (1977b, Chapters 1 and 9).