# .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

(0.005 seconds)

## 1—10 of 794 matching pages

##### 1: 19.2 Definitions
where $p_{j}$ is a polynomial in $t$ while $\rho$ and $\sigma$ are rational functions of $t$. … Here $a,b,p$ are real parameters, and $k_{c}$ and $x$ are real or complex variables, with $p\neq 0$, $k_{c}\neq 0$. … If $1, then $k_{c}$ is pure imaginary. …
###### §19.2(iv) A Related Function: $R_{C}\left(x,y\right)$
For the special cases of $R_{C}\left(x,x\right)$ and $R_{C}\left(0,y\right)$ see (19.6.15). …
##### 2: 34.6 Definition: $\mathit{9j}$ Symbol
###### §34.6 Definition: $\mathit{9j}$ Symbol
The $\mathit{9j}$ symbol may be defined either in terms of $\mathit{3j}$ symbols or equivalently in terms of $\mathit{6j}$ symbols:
34.6.1 $\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{21}&j_{22}&j_{23}\\ j_{31}&j_{32}&j_{33}\end{Bmatrix}=\sum_{\mbox{\scriptsize all }m_{rs}}\begin{% pmatrix}j_{11}&j_{12}&j_{13}\\ m_{11}&m_{12}&m_{13}\end{pmatrix}\begin{pmatrix}j_{21}&j_{22}&j_{23}\\ m_{21}&m_{22}&m_{23}\end{pmatrix}\begin{pmatrix}j_{31}&j_{32}&j_{33}\\ m_{31}&m_{32}&m_{33}\end{pmatrix}\*\begin{pmatrix}j_{11}&j_{21}&j_{31}\\ m_{11}&m_{21}&m_{31}\end{pmatrix}\begin{pmatrix}j_{12}&j_{22}&j_{32}\\ m_{12}&m_{22}&m_{32}\end{pmatrix}\begin{pmatrix}j_{13}&j_{23}&j_{33}\\ m_{13}&m_{23}&m_{33}\end{pmatrix},$
34.6.2 $\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{21}&j_{22}&j_{23}\\ j_{31}&j_{32}&j_{33}\end{Bmatrix}=\sum_{j}(-1)^{2j}(2j+1)\begin{Bmatrix}j_{11}% &j_{21}&j_{31}\\ j_{32}&j_{33}&j\end{Bmatrix}\begin{Bmatrix}j_{12}&j_{22}&j_{32}\\ j_{21}&j&j_{23}\end{Bmatrix}\begin{Bmatrix}j_{13}&j_{23}&j_{33}\\ j&j_{11}&j_{12}\end{Bmatrix}.$
The $\mathit{9j}$ 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: $\mathit{9j}$ Symbol
###### §34.7(vi) Sums
It constitutes an addition theorem for the $\mathit{9j}$ symbol. …
##### 4: 26.9 Integer Partitions: Restricted Number and Part Size
$p_{k}\left(n\right)$ denotes the number of partitions of $n$ into at most $k$ parts. See Table 26.9.1. … It follows that $p_{k}\left(n\right)$ also equals the number of partitions of $n$ into parts that are less than or equal to $k$. $p_{k}\left(\leq m,n\right)$ 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 $a_{m}\left(q\right)$ and $b_{m}\left(q\right)$ for $m\leq 6$ are: … The coefficients of the power series of $a_{2n}\left(q\right)$, $b_{2n}\left(q\right)$ and also $a_{2n+1}\left(q\right)$, $b_{2n+1}\left(q\right)$ are the same until the terms in $q^{2n-2}$ and $q^{2n}$, respectively. … Numerical values of the radii of convergence $\rho_{n}^{(j)}$ of the power series (28.6.1)–(28.6.14) for $n=0,1,\dots,9$ are given in Table 28.6.1. Here $j=1$ for $a_{2n}\left(q\right)$, $j=2$ for $b_{2n+2}\left(q\right)$, and $j=3$ for $a_{2n+1}\left(q\right)$ and $b_{2n+1}\left(q\right)$. …
##### 7: 34.1 Special Notation
The main functions treated in this chapter are the Wigner $\mathit{3j},\mathit{6j},\mathit{9j}$ symbols, respectively,
$\begin{pmatrix}j_{1}&j_{2}&j_{3}\\ m_{1}&m_{2}&m_{3}\end{pmatrix},$
$\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{21}&j_{22}&j_{23}\\ j_{31}&j_{32}&j_{33}\end{Bmatrix}.$
An often used alternative to the $\mathit{3j}$ symbol is the Clebsch–Gordan coefficient …For other notations for $\mathit{3j}$, $\mathit{6j}$, $\mathit{9j}$ 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 $p_{1},p_{2},\dots,p_{\nu\left(n\right)}$ are the distinct prime factors of $n$, each exponent $a_{r}$ is positive, and $\nu\left(n\right)$ is the number of distinct primes dividing $n$. … Note that $\sigma_{0}\left(n\right)=d\left(n\right)$. …Note that $J_{1}\left(n\right)=\phi\left(n\right)$. In the following examples, $a_{1},\dots,a_{\nu\left(n\right)}$ 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
$\mathfrak{S}_{S}$ denotes the set of permutations of $S$ for all distinct orderings of the $a_{1}+a_{2}+\cdots+a_{n}$ integers. The number of elements in $\mathfrak{S}_{S}$ is the multinomial coefficient (§26.4) $\genfrac{(}{)}{0.0pt}{}{a_{1}+a_{2}+\cdots+a_{n}}{a_{1},a_{2},\ldots,a_{n}}$. … Thus $\mathop{\mathrm{inv}}(351322453154)=4+8+0+3+1+1+2+3+1+0+1=24$, and $\mathop{\mathrm{maj}}(351322453154)=2+4+8+9+11=34.$ The $q$-multinomial coefficient is defined in terms of Gaussian polynomials (§26.9(ii)) by …and again with $S=\{1^{a_{1}},2^{a_{2}},\ldots,n^{a_{n}}\}$ we have …
##### 10: 10.75 Tables
• Abramowitz and Stegun (1964, Chapter 9) tabulates $j_{n,m}$, $J_{n}'\left(j_{n,m}\right)$, ${j^{\prime}_{n,m}}$, $J_{n}\left({j^{\prime}_{n,m}}\right)$, $n=0(1)8$, $m=1(1)20$, 5D (10D for $n=0$), $y_{n,m}$, $Y_{n}'\left(y_{n,m}\right)$, ${y^{\prime}_{n,m}}$, $Y_{n}\left({y^{\prime}_{n,m}}\right)$, $n=0(1)8$, $m=1(1)20$, 5D (8D for $n=0$), $J_{0}\left(j_{0,m}x\right)$, $m=1(1)5$, $x=0(.02)1$, 5D. Also included are the first 5 zeros of the functions $xJ_{1}\left(x\right)-\lambda J_{0}\left(x\right)$, $J_{1}\left(x\right)-\lambda xJ_{0}\left(x\right)$, $J_{0}\left(x\right)Y_{0}\left(\lambda x\right)-Y_{0}\left(x\right)J_{0}\left(% \lambda x\right)$, $J_{1}\left(x\right)Y_{1}\left(\lambda x\right)-Y_{1}\left(x\right)J_{1}\left(% \lambda x\right)$, $J_{1}\left(x\right)Y_{0}\left(\lambda x\right)-Y_{1}\left(x\right)J_{0}\left(% \lambda x\right)$ for various values of $\lambda$ and $\lambda^{-1}$ in the interval $[0,1]$, 4–8D.

• Makinouchi (1966) tabulates all values of $j_{\nu,m}$ and $y_{\nu,m}$ in the interval $(0,100)$, with at least 29S. These are for $\nu=0(1)5$, 10, 20; $\nu=\tfrac{3}{2}$, $\tfrac{5}{2}$; $\nu=m/n$ with $m=1(1)n-1$ and $n=3(1)8$, except for $\nu=\tfrac{1}{2}$.

• Abramowitz and Stegun (1964, Chapter 11) tabulates $\int_{0}^{x}J_{0}\left(t\right)\,\mathrm{d}t$, $\int_{0}^{x}Y_{0}\left(t\right)\,\mathrm{d}t$, $x=0(.1)10$, 10D; $\int_{0}^{x}t^{-1}(1-J_{0}\left(t\right))\,\mathrm{d}t$, $\int_{x}^{\infty}t^{-1}Y_{0}\left(t\right)\,\mathrm{d}t$, $x=0(.1)5$, 8D.

• Leung and Ghaderpanah (1979), tabulates all zeros of the principal value of $K_{n}\left(z\right)$, for $n=2(1)10$, 29S.

• Abramowitz and Stegun (1964, Chapter 11) tabulates $e^{-x}\int_{0}^{x}I_{0}\left(t\right)\,\mathrm{d}t$, $e^{x}\int_{x}^{\infty}K_{0}\left(t\right)\,\mathrm{d}t$, $x=0(.1)10$, 7D; $e^{-x}\int_{0}^{x}t^{-1}(I_{0}\left(t\right)-1)\,\mathrm{d}t$, $xe^{x}\int_{x}^{\infty}t^{-1}K_{0}\left(t\right)\,\mathrm{d}t$, $x=0(.1)5$, 6D.