# squares and products

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## 1—10 of 33 matching pages

##### 1: 18.36 Miscellaneous Polynomials
Sobolev OP’s are orthogonal with respect to an inner product involving derivatives. … These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. …
##### 2: 26.12 Plane Partitions
26.12.10 $\left(\prod_{h=1}^{r}\prod_{j=1}^{s}\frac{h+j+t-1}{h+j-1}\right)\*\left(\prod_% {h=1}^{r+1}\prod_{j=1}^{s}\frac{h+j+t-1}{h+j-1}\right);$
26.12.11 $\left(\prod_{h=1}^{r+1}\prod_{j=1}^{s}\frac{h+j+t-1}{h+j-1}\right)\*\left(% \prod_{h=1}^{r}\prod_{j=1}^{s+1}\frac{h+j+t-1}{h+j-1}\right).$
where $\sigma_{2}(j)$ is the sum of the squares of the divisors of $j$. …
##### 3: 20.12 Mathematical Applications
For applications of $\theta_{3}\left(0,q\right)$ to problems involving sums of squares of integers see §27.13(iv), and for extensions see Estermann (1959), Serre (1973, pp. 106–109), Koblitz (1993, pp. 176–177), and McKean and Moll (1999, pp. 142–143). For applications of Jacobi’s triple product (20.5.9) to Ramanujan’s $\tau\left(n\right)$ function and Euler’s pentagonal numbers see Hardy and Wright (1979, pp. 132–160) and McKean and Moll (1999, pp. 143–145). …
##### 4: 27.6 Divisor Sums
27.6.1 $\sum_{d\mathbin{|}n}\lambda\left(d\right)=\begin{cases}1,&n\mbox{ is a square}% ,\\ 0,&\mbox{otherwise}.\end{cases}$
27.6.2 $\sum_{d\mathbin{|}n}\mu\left(d\right)f(d)=\prod_{p\mathbin{|}n}(1-f(p)),$ $n>1$.
Generating functions, Euler products, and Möbius inversion are used to evaluate many sums extended over divisors. …
##### 9: DLMF Project News
error generating summary
##### 10: 20.7 Identities
###### §20.7(iv) Reduction Formulas for Products
In the following equations $\tau^{\prime}=-1/\tau$, and all square roots assume their principal values. …