# of reciprocals

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27.9.2 $(2|p)=(-1)^{(p^{2}-1)/8}.$
If $p,q$ are distinct odd primes, then the quadratic reciprocity law states that … Both (27.9.1) and (27.9.2) are valid with $p$ replaced by $P$; the reciprocity law (27.9.3) holds if $p,q$ are replaced by any two relatively prime odd integers $P,Q$.
##### 3: 8.23 Statistical Applications
In queueing theory the Erlang loss function is used, which can be expressed in terms of the reciprocal of $Q\left(a,x\right)$; see Jagerman (1974) and Cooper (1981, pp. 80, 316–319). …
##### 4: 5.2 Definitions
5.2.1 $\Gamma\left(z\right)=\int_{0}^{\infty}e^{-t}t^{z-1}\,\mathrm{d}t,$ $\Re z>0$.
##### 5: 27.14 Unrestricted Partitions
Euler introduced the reciprocal of the infinite product
27.14.2 $\mathit{f}\left(x\right)=\prod_{m=1}^{\infty}(1-x^{m})=\left(x;x\right)_{% \infty},$ $|x|<1$,
27.14.4 $\mathit{f}\left(x\right)=1-x-x^{2}+x^{5}+x^{7}-x^{12}-x^{15}+\dots=1+\sum_{k=1% }^{\infty}(-1)^{k}\left(x^{\omega(k)}+x^{\omega(-k)}\right),$
27.14.15 $5\frac{(\mathit{f}\left(x^{5}\right))^{5}}{(\mathit{f}\left(x\right))^{6}}=% \sum_{n=0}^{\infty}p\left(5n+4\right)x^{n}$
##### 7: 5.8 Infinite Products
5.8.3 $\left|\frac{\Gamma\left(x\right)}{\Gamma\left(x+\mathrm{i}y\right)}\right|^{2}% =\prod_{k=0}^{\infty}\left(1+\frac{y^{2}}{(x+k)^{2}}\right),$ $x\neq 0,-1,\dots$.
##### 8: 5.23 Approximations
Clenshaw (1962) also gives 20D Chebyshev-series coefficients for $\Gamma\left(1+x\right)$ and its reciprocal for $0\leq x\leq 1$. …
##### 9: 19.31 Probability Distributions
$R_{G}\left(x,y,z\right)$ and $R_{F}\left(x,y,z\right)$ occur as the expectation values, relative to a normal probability distribution in ${\mathbb{R}}^{2}$ or ${\mathbb{R}}^{3}$, of the square root or reciprocal square root of a quadratic form. …
##### 10: 27.16 Cryptography
To do this, let $s$ denote the reciprocal of $r$ modulo $\phi\left(n\right)$, so that $rs=1+t\phi\left(n\right)$ for some integer $t$. …