hypergeom(n,d,z) is the generalized hypergeometric function F(n, d, z), also known as the Barnes extended hypergeometric function and denoted by _jF_k where j = length(n) and k = length(d). For scalar a, b, and c, hypergeom([a,b],c,z) is the Gauss hypergeometric function ₂F₁(a,b;c;z).

The definition by a formal power series is

where

Either of the first two arguments may be a vector providing the coefficient parameters for a single function evaluation. If the third argument is a vector, the function is evaluated point-wise. The result is numeric if all the arguments are numeric and symbolic if any of the arguments is symbolic.

Examples

Compute hypergeometric functions:

syms a z
q = hypergeom([],[],z)
r = hypergeom(1,[],z)
s = hypergeom(a,[],z)

The results are:

q =
exp(z)
 
r =
-1/(z - 1)
 
s =
1/(1 - z)^a

References

Oberhettinger, F. "Hypergeometric Functions." Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. (M. Abramowitz and I. A. Stegun, eds.). New York: Dover, 1972.

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