哪里能办北卡罗莱纳州驾照【仿证微kaa77788】】el2

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… ►For research software see Bulirsch (1965b, function

\operatorname{el2}

), Bulirsch (1969b, function

\operatorname{el3}

), Jefferson (1961), and Neuman (1969a, functions

E\left(\phi,k\right)

and

\Pi\left(\phi,k^{2},k\right)

). …

… ►

\operatorname{el2}\left(x,k_{c},a,b\right),

…

… ►

19.2.12

\operatorname{el2}\left(x,k_{c},a,b\right)=\int_{0}^{\operatorname{arctan}x}% \frac{a+b{\tan}^{2}\theta}{\sqrt{(1+{\tan}^{2}\theta)(1+k_{c}^{2}{\tan}^{2}% \theta)}}\,\mathrm{d}\theta.

ⓘ

Defines:: $\operatorname{el2}\left(\NVar{x},\NVar{k_{c}},\NVar{a},\NVar{b}\right)$ : Bulirsch’s incomplete elliptic integral of the second kind
Symbols:: $\,\mathrm{d}\NVar{x}$ : differential of $x$ , $\int$ : integral, $\operatorname{arctan}\NVar{z}$ : arctangent function, $\tan\NVar{z}$ : tangent function, $a$ : real parameter, $b$ : real parameter, $k_{c}$ : real or complex variable not equal to zero and $x$ : real or complex variable
Permalink:: http://dlmf.nist.gov/19.2.E12
Encodings:: pMML, png, TeX
See also:: Annotations for §19.2(iii), §19.2 and Ch.19

… ►

F\left(\phi,k\right)=\operatorname{el1}\left(x,k_{c}\right)=\operatorname{el2}% \left(x,k_{c},1,1\right),

►

E\left(\phi,k\right)=\operatorname{el2}\left(x,k_{c},1,k_{c}^{2}\right),

►

D\left(\phi,k\right)=\operatorname{el2}\left(x,k_{c},0,1\right).

…

… ►The function

\operatorname{el2}\left(x,k_{c},a,b\right)

is computed by descending Landen transformations if

x

is real, or by descending Gauss transformations if

x

is complex (Bulirsch (1965b)). …

… ►

19.25.21

\operatorname{el2}\left(x,k_{c},a,b\right)=a\operatorname{el1}\left(x,k_{c}% \right)+\tfrac{1}{3}{(b-a)}R_{D}\left(r,r+k_{c}^{2},r+1\right),

ⓘ

Symbols:: $\operatorname{el1}\left(\NVar{x},\NVar{k_{c}}\right)$ : Bulirsch’s incomplete elliptic integral of the first kind, $\operatorname{el2}\left(\NVar{x},\NVar{k_{c}},\NVar{a},\NVar{b}\right)$ : Bulirsch’s incomplete elliptic integral of the second kind, $R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)$ : elliptic integral symmetric in only two variables, $k$ : real or complex modulus and $r$ : inverse
Permalink:: http://dlmf.nist.gov/19.25.E21
Encodings:: pMML, png, TeX
See also:: Annotations for §19.25(ii), §19.25 and Ch.19

…