About the Project

.%E5%B9%BF%E5%B7%9E%E5%B9%B4%E4%B8%96%E7%95%8C%E6%9D%AF%E7%9C%8B%E7%90%83%E9%85%92%E5%90%A7_%E3%80%8Ewn4.com_%E3%80%8F%E4%B8%96%E7%95%8C%E6%9D%AF%E6%9C%89%E5%A5%B3%E8%B6%B3%E5%90%97_w6n2c9o_2022%E5%B9%B411%E6%9C%8829%E6%97%A57%E6%97%B615%E5%88%8646%E7%A7%92_p5nl57rxz_gov_hk

AdvancedHelp

Did you mean .%E5%B9%BF%E5%B7%9E%E5%B9%B4%E4%B8%96%E7%95%8C%E6%9D%AF%E7%9C%8B%E7%90%83%E9%85%92%E5%90%A7_%E3%80%8Ewn4.com_%E3%80%8F%E4%B8%96%E7%95%8C%E6%9D%AF%E6%9C%89%E5%A5%B3%E8%B6%B3%E5%90%97_w6n2c9o_2022%E5%B9%411%E6%9C%882%E6%97%157%E6%97%615%E5%88%864%E7%A7%92_p5nl57rxz_gov_hk ?

(0.037 seconds)

1—10 of 602 matching pages

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: 9.2 Differential Equation
3: 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).
4: 9 Airy and Related Functions
Chapter 9 Airy and Related Functions
5: 24.2 Definitions and Generating Functions
E 2 n + 1 = 0 ,
24.2.9 E n = 2 n E n ( 1 2 ) = integer ,
E ~ n ( x ) = E n ( x ) , 0 x < 1 ,
E ~ n ( x + 1 ) = E ~ n ( x ) , x .
Table 24.2.4: Euler numbers E n .
n E n
6: 8.26 Tables
  • Abramowitz and Stegun (1964, pp. 245–248) tabulates E n ( x ) for n = 2 , 3 , 4 , 10 , 20 , x = 0 ( .01 ) 2 to 7D; also ( x + n ) e x E n ( x ) for n = 2 , 3 , 4 , 10 , 20 , x 1 = 0 ( .01 ) 0.1 ( .05 ) 0.5 to 6S.

  • Chiccoli et al. (1988) presents a short table of E p ( x ) for p = 9 2 ( 1 ) 1 2 , 0 x 200 to 14S.

  • Pagurova (1961) tabulates E n ( x ) for n = 0 ( 1 ) 20 , x = 0 ( .01 ) 2 ( .1 ) 10 to 4-9S; e x E n ( x ) for n = 2 ( 1 ) 10 , x = 10 ( .1 ) 20 to 7D; e x E p ( x ) for p = 0 ( .1 ) 1 , x = 0.01 ( .01 ) 7 ( .05 ) 12 ( .1 ) 20 to 7S or 7D.

  • Stankiewicz (1968) tabulates E n ( x ) for n = 1 ( 1 ) 10 , x = 0.01 ( .01 ) 5 to 7D.

  • Zhang and Jin (1996, Table 19.1) tabulates E n ( x ) for n = 1 , 2 , 3 , 5 , 10 , 15 , 20 , x = 0 ( .1 ) 1 , 1.5 , 2 , 3 , 5 , 10 , 20 , 30 , 50 , 100 to 7D or 8S.

  • 7: 34 3j, 6j, 9j Symbols
    Chapter 34 3 j , 6 j , 9 j Symbols
    8: 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. …
    9: 19.36 Methods of Computation
    where the elementary symmetric functions E s are defined by (19.19.4). … Accurate values of F ( ϕ , k ) E ( ϕ , k ) for k 2 near 0 can be obtained from R D by (19.2.6) and (19.25.13). … E ( ϕ , k ) can be evaluated by using (19.25.7), and R D by using (19.21.10), but cancellations may become significant. Thompson (1997, pp. 499, 504) uses descending Landen transformations for both F ( ϕ , k ) and E ( ϕ , k ) . … Lee (1990) compares the use of theta functions for computation of K ( k ) , E ( k ) , and K ( k ) E ( k ) , 0 k 2 1 , with four other methods. …
    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).