Mathematical constants
----------------------

Mpmath supports arbitrary-precision computation of various common (and less common) mathematical constants. These constants are implemented as lazy objects that can be computed with any precision. Whenever the objects are used as function arguments or as operands in arithmetic operations, they automagically evaluate to the current working precision. A lazy number can be converted to a regular ``mpf`` using the unary ``+`` operator::

    >>> from mpmath import *
    >>> mp.dps = 15
    >>> pi
    <pi: 3.14159~>
    >>> 2*pi
    mpf('6.2831853071795862')
    >>> +pi
    mpf('3.1415926535897931')
    >>> mp.dps = 40
    >>> pi
    <pi: 3.14159~>
    >>> 2*pi
    mpf('6.283185307179586476925286766559005768394338')
    >>> +pi
    mpf('3.141592653589793238462643383279502884197169')

Exact constants
...............

The predefined objects :data:`j` (imaginary unit), :data:`inf` (positive infinity) and :data:`nan` (not-a-number) are shortcuts to :class:`mpc` and :class:`mpf` instances with these fixed values.

Pi (``pi``)
....................................

.. autoattribute:: mpmath.functions.pi

Degree (``degree``)
....................................

.. autoattribute:: mpmath.functions.degree

Base of the natural logarithm (``e``)
.....................................

.. autoattribute:: mpmath.functions.e

Golden ratio (``phi``)
......................

.. autoattribute:: mpmath.functions.phi


Euler's constant (``euler``)
............................

.. autoattribute:: mpmath.functions.euler

Catalan's constant (``catalan``)
................................

.. autoattribute:: mpmath.functions.catalan

Apery's constant (``apery``)
............................

.. autoattribute:: mpmath.functions.apery

Khinchin's constant (``khinchin``)
..................................

.. autoattribute:: mpmath.functions.khinchin

Glaisher's constant (``glaisher``)
..................................

.. autoattribute:: mpmath.functions.glaisher
