hypergeometric( [ a1 , ... ] , [ b1 , ... ] , z )

The generalized hypergeometric function of z in SageMath. Defined by

$\,_p F _q \left( \begin{matrix} a_1 , \ldots , a_p \\ b_1 , \dots , b_q \end{matrix} ; z \right) = \sum_{k=0}^\infty \frac{ (a_1)_k \cdots (a_p)_k }{ (b_1)_k \cdots (b_p)_k } \frac{ z^k }{ k! }$

with the rising factorial

$(a)_k = a(a+1) \cdots (a+k-1) = \frac{ \Gamma(a+k) }{ \Gamma(a) }$

The two sets of parameters must be given as lists.

Plots on the real axis:

real( hypergeometric([a,b],[c],x) )

imag( hypergeometric([a,b],[c],x) )