About the Project

.广州年世界杯看球酒吧_『wn4.com_』世界杯有女足吗_w6n2c9o_2022年11月29日7时15分46秒_p5nl57rxz_gov_hk

AdvancedHelp

Did you mean .广州年世界杯看球酒吧_『welcom_』世界杯有女足吗_w6n2c9o_2022年11月29日7时15分46秒_p5nl57rxz_gov_hk ?

(0.007 seconds)

1—10 of 779 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
34.6.1 { 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 } .
3: 34.7 Basic Properties: 9 j Symbol
34.7.1 { j 11 j 12 j 13 j 21 j 22 j 13 j 31 j 31 0 } = ( 1 ) j 12 + j 21 + j 13 + j 31 ( ( 2 j 13 + 1 ) ( 2 j 31 + 1 ) ) 1 2 { j 11 j 12 j 13 j 22 j 21 j 31 } .
34.7.2 j 12 j 34 ( 2 j 12 + 1 ) ( 2 j 34 + 1 ) ( 2 j 13 + 1 ) ( 2 j 24 + 1 ) { j 1 j 2 j 12 j 3 j 4 j 34 j 13 j 24 j } { j 1 j 2 j 12 j 3 j 4 j 34 j 13 j 24 j } = δ j 13 , j 13 δ j 24 , j 24 .
34.7.3 j 13 j 24 ( 1 ) 2 j 2 + j 24 + j 23 j 34 ( 2 j 13 + 1 ) ( 2 j 24 + 1 ) { j 1 j 2 j 12 j 3 j 4 j 34 j 13 j 24 j } { j 1 j 3 j 13 j 4 j 2 j 24 j 14 j 23 j } = { j 1 j 2 j 12 j 4 j 3 j 34 j 14 j 23 j } .
34.7.4 ( j 13 j 23 j 33 m 13 m 23 m 33 ) { j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33 } = m r 1 , m r 2 , r = 1 , 2 , 3 ( 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 ) .
34.7.5 j ( 2 j + 1 ) { j 11 j 12 j j 21 j 22 j 23 j 31 j 32 j 33 } { j 11 j 12 j j 23 j 33 j } = ( 1 ) 2 j { j 21 j 22 j 23 j 12 j j 32 } { j 31 j 32 j 33 j j 11 j 21 } .
4: 34.1 Special Notation
( 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
34.1.1 ( j 1 m 1 j 2 m 2 | j 1 j 2 j 3 m 3 ) = ( 1 ) j 1 j 2 + m 3 ( 2 j 3 + 1 ) 1 2 ( j 1 j 2 j 3 m 1 m 2 m 3 ) ;
see Edmonds (1974, p. 46, Eq. (3.7.3)) and Rotenberg et al. (1959, p. 1, Eq. (1.1a)). …
5: 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 . …
6: 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 . …
7: 26.16 Multiset Permutations
Let S = { 1 a 1 , 2 a 2 , , n a n } be the multiset that has a j copies of j , 1 j n . 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 ) . … 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 …
8: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
( n n 1 , n 2 , , n k ) is the number of ways of placing n = n 1 + n 2 + + n k distinct objects into k labeled boxes so that there are n j objects in the j th box. … These are given by the following equations in which a 1 , a 2 , , a n are nonnegative integers such that … M 1 is the multinominal coefficient (26.4.2): …For each n all possible values of a 1 , a 2 , , a n are covered. … where the summation is over all nonnegative integers n 1 , n 2 , , n k such that n 1 + n 2 + + n k = n . …
9: 1.3 Determinants
The cofactor A j k of a j k is … For real-valued a j k , … where ω 1 , ω 2 , , ω n are the n th roots of unity (1.11.21). … If 𝐷 n [ a j , k ] tends to a limit L as n , then we say that the infinite determinant 𝐷 [ a j , k ] converges and 𝐷 [ a j , k ] = L . … Here δ j , k is the Kronecker delta. …
10: 34.3 Basic Properties: 3 j Symbol
When any one of j 1 , j 2 , j 3 is equal to 0 , 1 2 , or 1 , the 3 j symbol has a simple algebraic form. …For these and other results, and also cases in which any one of j 1 , j 2 , j 3 is 3 2 or 2 , see Edmonds (1974, pp. 125–127). … Even permutations of columns of a 3 j symbol leave it unchanged; odd permutations of columns produce a phase factor ( 1 ) j 1 + j 2 + j 3 , for example,
34.3.8 ( j 1 j 2 j 3 m 1 m 2 m 3 ) = ( j 2 j 3 j 1 m 2 m 3 m 1 ) = ( j 3 j 1 j 2 m 3 m 1 m 2 ) ,
For the polynomials P l see §18.3, and for the function Y l , m see §14.30. …