Numeric Constants

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#### Numeric Constants

##### Synopsis

    #include <boost/math/constants/constants.hpp>

    namespace boost{ namespace math{ namespace constants{

    template <class T> T pi();
    template <class T> T root_pi();
    template <class T> T root_half_pi();
    template <class T> T root_two_pi();
    template <class T> T root_ln_four();
    template <class T> T e();
    template <class T> T half();
    template <class T> T euler();
    template <class T> T root_two();
    template <class T> T ln_two();
    template <class T> T ln_ln_two();
    template <class T> T third();
    template <class T> T twothirds();
    template <class T> T pi_minus_three();
    template <class T> T four_minus_pi();

    }}} // namespaces

##### Description

The header `boost/math/constants/constants.hpp` contains some numeric constants that we have found useful in the development of this library. New constants are added on an ad-hock basis based on need.

Usage is like this:

    template <class T>
    T circumference(T r)
    {
       return 2 * boost::math::constants::pi<T>() * r;
    }

All the constants are accurate to at least the 34 decimal digits required for 128-bit long doubles, and most are accurate to 100 digits or more when used with a suitable arbitrary precision type.

The following table summarises the constants we have at present:

Constant | Meaning | Value
--- | --- | ---
pi | π | 3.1415926535897932384...
root_pi | √π | 1.772453850905516027...
root_half_pi | √(π/2) | 1.253314137315500251...
root_two_pi | √(2*π) | 2.506628274631000502...
root_ln_four | √(ln(4)) | 1.17741002251547469...
e | e | 2.71828182845904523536...
half | 0.5 | 0.5
euler | Euler's constant | 0.577215664901532860606
root_two | √2 | 1.4142135623730950488...
ln_two | ln(2) | 0.6931471805599453094...
ln_ln_two | ln(ln(2)) | -0.3665129205816643...
third | 1/3 | 0.333333333333333333...
twothirds | 2/3 | 0.666666666666666666...
pi_minus_three | π-3 | 0.14159265358979323846...
four_minus_pi | 4-π | 0.85840734641020676153735...