英苏布里亚大学硕士证书【购证 微kaa77788】put

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1: 26.17 The Twelvefold Way

… ►The twelvefold way gives the number of mappings $f$ from set $N$ of $n$ objects to set $K$ of $k$ objects (putting balls from set $N$ into boxes in set $K$). …

2: Guide to Searching the DLMF

… ►Be careful, however, because if you put quotes around math expressions involving math symbols, you may not get the matches you’d expect. …

3: 19.22 Quadratic Transformations

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4: 26.13 Permutations: Cycle Notation

… ►In cycle notation, the elements in each cycle are put inside parentheses, ordered so that $\sigma (j)$ immediately follows $j$ or, if $j$ is the last listed element of the cycle, then $\sigma (j)$ is the first element of the cycle. …

5: 19.17 Graphics

… ►To view $R_F(0,y,1)$ and $2R_G(0,y,1)$ for complex $y$, put $y=1-k^2$, use (19.25.1), and see Figures 19.3.7–19.3.12. … ►To view $R_F(0,y,1)$ and $2R_G(0,y,1)$ for complex $y$, put $y=1-k^2$, use (19.25.1), and see Figures 19.3.7–19.3.12. …

6: 19.28 Integrals of Elliptic Integrals

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7: 19.20 Special Cases

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8: 19.26 Addition Theorems

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9: 19.3 Graphics

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Figure 19.3.3: $F(\varphi ,k)$ as a function of $k^2$ and ${\sin }^2\varphi$ for $-1\le k^2\le 2$, $0\le {\sin }^2\varphi \le 1$. …If ${\sin }^2\varphi =1/k^2$ (), then it has the value $K\left(1/k\right)/k$: put $c=k^2$ in (19.25.5) and use (19.25.1). Magnify 3D Help

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Figure 19.3.4: $E(\varphi ,k)$ as a function of $k^2$ and ${\sin }^2\varphi$ for $-1\le k^2\le 2$, $0\le {\sin }^2\varphi \le 1$. …If ${\sin }^2\varphi =1/k^2$ (), then it has the value $kE\left(1/k\right)+(k_{}^{\prime }{}_{}{}^2/k)K\left(1/k\right)$, with limit 1 as $k^2\to 1+$: put $c=k^2$ in (19.25.7) and use (19.25.1). Magnify 3D Help

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10: 19.21 Connection Formulas

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