About the Project

.世界杯 买球怎么买_『wn4.com_』2018世界杯一共多少支球队_w6n2c9o_2022年11月29日6时48分9秒_ok040qquy_gov_hk

AdvancedHelp

Did you mean .世界杯 买球怎么买_『welcom_』2018世界杯一共多少支球队_w6n2c9o_2022年11月29日6时48分9秒_ok040qquy_gov_hk ?

(0.005 seconds)

1—10 of 794 matching pages

1: 19.2 Definitions
where p j is a polynomial in t while ρ and σ are rational functions of t . … Here a , b , p are real parameters, and k c and x are real or complex variables, with p 0 , k c 0 . … If 1 < k 1 / sin ϕ , then k c is pure imaginary. …
§19.2(iv) A Related Function: R C ( x , y )
For the special cases of R C ( x , x ) and R C ( 0 , y ) see (19.6.15). …
2: 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. …
3: 34.7 Basic Properties: 9 j Symbol
§34.7 Basic Properties: 9 j Symbol
§34.7(ii) Symmetry
§34.7(iv) Orthogonality
§34.7(vi) Sums
It constitutes an addition theorem for the 9 j symbol. …
4: 26.9 Integer Partitions: Restricted Number and Part Size
p k ( n ) denotes the number of partitions of n into at most k parts. See Table 26.9.1. … It follows that p k ( n ) also equals the number of partitions of n into parts that are less than or equal to k . p k ( m , n ) is the number of partitions of n into at most k parts, each less than or equal to m . …
5: 28.6 Expansions for Small q
Leading terms of the power series for a m ( q ) and b m ( q ) for m 6 are: … The coefficients of the power series of a 2 n ( q ) , b 2 n ( q ) and also a 2 n + 1 ( q ) , b 2 n + 1 ( q ) are the same until the terms in q 2 n 2 and q 2 n , respectively. … Numerical values of the radii of convergence ρ n ( j ) of the power series (28.6.1)–(28.6.14) for n = 0 , 1 , , 9 are given in Table 28.6.1. Here j = 1 for a 2 n ( q ) , j = 2 for b 2 n + 2 ( q ) , and j = 3 for a 2 n + 1 ( q ) and b 2 n + 1 ( q ) . …
§28.6(ii) Functions ce n and se n
6: 10 Bessel Functions
7: 34.1 Special Notation
The main functions treated in this chapter are the Wigner 3 j , 6 j , 9 j symbols, respectively,
( j 1 j 2 j 3 m 1 m 2 m 3 ) ,
{ j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33 } .
An often used alternative to the 3 j symbol is the Clebsch–Gordan coefficient …For other notations for 3 j , 6 j , 9 j symbols, see Edmonds (1974, pp. 52, 97, 104–105) and Varshalovich et al. (1988, §§8.11, 9.10, 10.10).
8: 27.2 Functions
where p 1 , p 2 , , p ν ( n ) are the distinct prime factors of n , each exponent a r is positive, and ν ( n ) is the number of distinct primes dividing n . … Note that σ 0 ( n ) = d ( n ) . …Note that J 1 ( n ) = ϕ ( n ) . In the following examples, a 1 , , a ν ( n ) are the exponents in the factorization of n in (27.2.1). … Table 27.2.1 lists the first 100 prime numbers p n . …
9: 26.16 Multiset Permutations
𝔖 S denotes the set of permutations of S for all distinct orderings of the a 1 + a 2 + + a n integers. The number of elements in 𝔖 S is the multinomial coefficient (§26.4) ( a 1 + a 2 + + a n a 1 , a 2 , , a n ) . … Thus inv ( 351322453154 ) = 4 + 8 + 0 + 3 + 1 + 1 + 2 + 3 + 1 + 0 + 1 = 24 , and maj ( 351322453154 ) = 2 + 4 + 8 + 9 + 11 = 34 . The q -multinomial coefficient is defined in terms of Gaussian polynomials (§26.9(ii)) by …and again with S = { 1 a 1 , 2 a 2 , , n a n } we have …
10: 10.75 Tables
  • Abramowitz and Stegun (1964, Chapter 9) tabulates j n , m , J n ( j n , m ) , j n , m , J n ( j n , m ) , n = 0 ( 1 ) 8 , m = 1 ( 1 ) 20 , 5D (10D for n = 0 ), y n , m , Y n ( y n , m ) , y n , m , Y n ( y n , m ) , n = 0 ( 1 ) 8 , m = 1 ( 1 ) 20 , 5D (8D for n = 0 ), J 0 ( j 0 , m x ) , m = 1 ( 1 ) 5 , x = 0 ( .02 ) 1 , 5D. Also included are the first 5 zeros of the functions x J 1 ( x ) λ J 0 ( x ) , J 1 ( x ) λ x J 0 ( x ) , J 0 ( x ) Y 0 ( λ x ) Y 0 ( x ) J 0 ( λ x ) , J 1 ( x ) Y 1 ( λ x ) Y 1 ( x ) J 1 ( λ x ) , J 1 ( x ) Y 0 ( λ x ) Y 1 ( x ) J 0 ( λ x ) for various values of λ and λ 1 in the interval [ 0 , 1 ] , 4–8D.

  • Makinouchi (1966) tabulates all values of j ν , m and y ν , m in the interval ( 0 , 100 ) , with at least 29S. These are for ν = 0 ( 1 ) 5 , 10, 20; ν = 3 2 , 5 2 ; ν = m / n with m = 1 ( 1 ) n 1 and n = 3 ( 1 ) 8 , except for ν = 1 2 .

  • Abramowitz and Stegun (1964, Chapter 11) tabulates 0 x J 0 ( t ) d t , 0 x Y 0 ( t ) d t , x = 0 ( .1 ) 10 , 10D; 0 x t 1 ( 1 J 0 ( t ) ) d t , x t 1 Y 0 ( t ) d t , x = 0 ( .1 ) 5 , 8D.

  • Leung and Ghaderpanah (1979), tabulates all zeros of the principal value of K n ( z ) , for n = 2 ( 1 ) 10 , 29S.

  • Abramowitz and Stegun (1964, Chapter 11) tabulates e x 0 x I 0 ( t ) d t , e x x K 0 ( t ) d t , x = 0 ( .1 ) 10 , 7D; e x 0 x t 1 ( I 0 ( t ) 1 ) d t , x e x x t 1 K 0 ( t ) d t , x = 0 ( .1 ) 5 , 6D.