Hypergeometric functions
------------------------

Common hypergeometric series
............................

For convenience, most of the hypergeometric series of low order are
provided as standalone functions. They can equivalently be evaluated using
:func:`hyper`. As will be demonstrated further in the individual docstrings,
all the following functions implement analytic continuations and/or asymptotic
expansions with respect to the argument `z`, thereby permitting evaluation
anywhere in the complex plane. Functions of higher degree can be computed
via :func:`hyper`, but generally only in rapidly convergent instances.

:func:`hyp0f1`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hyp0f1(a, z)

:func:`hyp1f1`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hyp1f1(a, b, z)

:func:`hyp1f2`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hyp1f2(a1, b1, b2, z)

:func:`hyp2f0`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hyp2f0(a, b, z)

:func:`hyp2f1`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hyp2f1(a, b, c, z)

:func:`hyp2f2`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hyp2f2(a1, a2, b1, b2, z)

:func:`hyp2f3`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hyp2f3(a1, a2, b1, b2, b3, z)

Generalized hypergeometric functions
....................................

:func:`hyper`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hyper(a_s, b_s, z)

:func:`hypercomb`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hypercomb

Confluent U and Whittaker functions
...................................

:func:`hyperu`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.hyperu(a, b, z)

:func:`whitm`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.whitm(k,m,z)

:func:`whitw`
^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.whitw(k,m,z)

Meijer G-function
...................................

:func:`meijerg`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.meijerg(a_s,b_s,z,r=1,**kwargs)

Appell hypergeometric function of two variables
...............................................

:func:`appellf1`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.functions.appellf1(a,b1,b2,c,x,y)
