About the Project

.2018年世界杯决赛裁判_『wn4.com_』1998年世界杯怎么了_w6n2c9o_2022年11月29日5时2分36秒_6ogsggucg_cc

AdvancedHelp

Did you mean .2018年世界杯决赛裁判_『welcom_』1998年世界杯怎么了_w6n2c9o_2022年11月29日5时2分36秒_6ogsggucg_cc ?

(0.007 seconds)

1—10 of 785 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: 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 . …
4: 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 } .
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: 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. …
7: 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 . …
8: 26.12 Plane Partitions
26.12.10 ( h = 1 r j = 1 s h + j + t 1 h + j 1 ) ( h = 1 r + 1 j = 1 s h + j + t 1 h + j 1 ) ;
26.12.11 ( h = 1 r + 1 j = 1 s h + j + t 1 h + j 1 ) ( h = 1 r j = 1 s + 1 h + j + t 1 h + j 1 ) .
The notation π B ( r , s , t ) denotes the sum over all plane partitions contained in B ( r , s , t ) , and | π | denotes the number of elements in π . … where σ 2 ( j ) is the sum of the squares of the divisors of j . …
26.12.26 pp ( n ) ( ζ ( 3 ) ) 7 / 36 2 11 / 36 ( 3 π ) 1 / 2 n 25 / 36 exp ( 3 ( ζ ( 3 ) ) 1 / 3 ( 1 2 n ) 2 / 3 + ζ ( 1 ) ) ,
9: 24.2 Definitions and Generating Functions
B 2 n + 1 = 0 ,
24.2.4 B n = B n ( 0 ) ,
Table 24.2.4: Euler numbers E n .
n E n
Table 24.2.5: Coefficients b n , k of the Bernoulli polynomials B n ( x ) = k = 0 n b n , k x k .
k
Table 24.2.6: Coefficients e n , k of the Euler polynomials E n ( x ) = k = 0 n e n , k x k .
k
10: Bibliography
  • M. Abramowitz (1949) Asymptotic expansions of spheroidal wave functions. J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
  • S. Ahmed and M. E. Muldoon (1980) On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations. Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.
  • A. Apelblat (1989) Derivatives and integrals with respect to the order of the Struve functions 𝐇 ν ( x ) and 𝐋 ν ( x ) . J. Math. Anal. Appl. 137 (1), pp. 17–36.
  • V. I. Arnol’d (1974) Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
  • R. Askey (1980) Some basic hypergeometric extensions of integrals of Selberg and Andrews. SIAM J. Math. Anal. 11 (6), pp. 938–951.