# sums of products

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##### 1: 27.1 Special Notation
 $d,k,m,n$ positive integers (unless otherwise indicated). … sum, product taken over divisors of $n$. … sum, product extended over all primes. …
##### 2: 15.17 Mathematical Applications
In combinatorics, hypergeometric identities classify single sums of products of binomial coefficients. …
##### 6: 34.4 Definition: $\mathit{6j}$ Symbol
The $\mathit{6j}$ symbol is defined by the following double sum of products of $\mathit{3j}$ symbols: …
34.4.2 $\begin{Bmatrix}j_{1}&j_{2}&j_{3}\\ l_{1}&l_{2}&l_{3}\end{Bmatrix}=\Delta(j_{1}j_{2}j_{3})\Delta(j_{1}l_{2}l_{3})% \Delta(l_{1}j_{2}l_{3})\Delta(l_{1}l_{2}j_{3})\*\sum_{s}\frac{(-1)^{s}(s+1)!}{% (s-j_{1}-j_{2}-j_{3})!(s-j_{1}-l_{2}-l_{3})!(s-l_{1}-j_{2}-l_{3})!(s-l_{1}-l_{% 2}-j_{3})!}\*\frac{1}{(j_{1}+j_{2}+l_{1}+l_{2}-s)!(j_{2}+j_{3}+l_{2}+l_{3}-s)!% (j_{3}+j_{1}+l_{3}+l_{1}-s)!},$
##### 7: 26.15 Permutations: Matrix Notation
The inversion number of $\sigma$ is a sum of products of pairs of entries in the matrix representation of $\sigma$: …
##### 8: Bibliography D
• K. Dilcher (1996) Sums of products of Bernoulli numbers. J. Number Theory 60 (1), pp. 23–41.
• ##### 9: 1.11 Zeros of Polynomials
The sum and product of the roots are respectively $-b/a$ and $c/a$. …
##### 10: 34.3 Basic Properties: $\mathit{3j}$ Symbol
For sums of products of $\mathit{3j}$ symbols, see Varshalovich et al. (1988, pp. 259–262). …