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橢圓積分 - 卡爾松(Carlson)形式

概要

```#include <boost/math/special_functions/ellint_rf.hpp>
```

```namespace boost { namespace math {

template <class T1, class T2, class T3>
calculated-result-type ellint_rf(T1 x, T2 y, T3 z)

template <class T1, class T2, class T3, class Policy>
calculated-result-type ellint_rf(T1 x, T2 y, T3 z, const Policy&)

}} // namespaces
```

```#include <boost/math/special_functions/ellint_rd.hpp>
```

```namespace boost { namespace math {

template <class T1, class T2, class T3>
calculated-result-type ellint_rd(T1 x, T2 y, T3 z)

template <class T1, class T2, class T3, class Policy>
calculated-result-type ellint_rd(T1 x, T2 y, T3 z, const Policy&)

}} // namespaces
```

```#include <boost/math/special_functions/ellint_rj.hpp>
```

```namespace boost { namespace math {

template <class T1, class T2, class T3, class T4>
calculated-result-type ellint_rj(T1 x, T2 y, T3 z, T4 p)

template <class T1, class T2, class T3, class T4, class Policy>
calculated-result-type ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy&)

}} // namespaces
```

```#include <boost/math/special_functions/ellint_rc.hpp>
```

```namespace boost { namespace math {

template <class T1, class T2>
calculated-result-type ellint_rc(T1 x, T2 y)

template <class T1, class T2, class Policy>
calculated-result-type ellint_rc(T1 x, T2 y, const Policy&)

}} // namespaces
```
說明

```template <class T1, class T2, class T3>
calculated-result-type ellint_rf(T1 x, T2 y, T3 z)

template <class T1, class T2, class T3, class Policy>
calculated-result-type ellint_rf(T1 x, T2 y, T3 z, const Policy&)
```

```template <class T1, class T2, class T3>
calculated-result-type ellint_rd(T1 x, T2 y, T3 z)

template <class T1, class T2, class T3, class Policy>
calculated-result-type ellint_rd(T1 x, T2 y, T3 z, const Policy&)
```

```template <class T1, class T2, class T3, class T4>
calculated-result-type ellint_rj(T1 x, T2 y, T3 z, T4 p)

template <class T1, class T2, class T3, class T4, class Policy>
calculated-result-type ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy&)
```

p < 0 時，這個函數使用下面的關係返回 柯蔚(Cauchy principal value) :

```template <class T1, class T2>
calculated-result-type ellint_rc(T1 x, T2 y)

template <class T1, class T2, class Policy>
calculated-result-type ellint_rc(T1 x, T2 y, const Policy&)
```

y < 0時， 這個函數使用下面的關係返回 柯蔚(Cauchy principal value) :

測試

B. C. Carlson, Numerical computation of real or complex elliptic integrals. Numerical Algorithms, Volume 10, Number 1 / March, 1995, pp 13-26.

精確性

RF

RD

RJ

RC

53

Win32 / Visual C++ 8.0

64

Red Hat Linux / G++ 3.4

113

HP-UX / HP aCC 6