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.hyp0f1(a, z) :func:`hyp1f1` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.hyp1f1(a, b, z) :func:`hyp1f2` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.hyp1f2(a1, b1, b2, z) :func:`hyp2f0` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.hyp2f0(a, b, z) :func:`hyp2f1` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.hyp2f1(a, b, c, z) :func:`hyp2f2` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.hyp2f2(a1, a2, b1, b2, z) :func:`hyp2f3` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.hyp2f3(a1, a2, b1, b2, b3, z) :func:`hyp3f2` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.hyp3f2(a1, a2, a3, b1, b2, z) Generalized hypergeometric functions .................................... :func:`hyper` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.hyper(a_s, b_s, z) :func:`hypercomb` ^^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.hypercomb Confluent U and Whittaker functions ................................... :func:`hyperu` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.hyperu(a, b, z) :func:`whitm` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.whitm(k,m,z) :func:`whitw` ^^^^^^^^^^^^^^ .. autofunction:: mpmath.whitw(k,m,z) Meijer G-function ................................... :func:`meijerg` ^^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.meijerg(a_s,b_s,z,r=1,**kwargs) Appell hypergeometric function of two variables ............................................... :func:`appellf1` ^^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.appellf1(a,b1,b2,c,x,y)