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11—20 of 31 matching pages

11: 19.20 Special Cases

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12: 19.26 Addition Theorems

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13: 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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14: 19.21 Connection Formulas

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15: 19.16 Definitions

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16: 18.40 Methods of Computation

… ►The quadrature points and weights can be put to a more direct and efficient use. …

17: 19.5 Maclaurin and Related Expansions

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18: 19.18 Derivatives and Differential Equations

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19: 19.23 Integral Representations

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20: 23.20 Mathematical Applications

… ►An algebraic curve that can be put either into the form …