Naively, the hypergeometric differential equation has two independent solutions as follows:
fun=y[x]/.DSolve[(x (1 - x) y''[x] + (c - (a + b + 1) x) y'[x] - a b y[x]) == 0, y[x], x][]
Let's say we are interested in obtaining the solution for
a,b,c integer, e.g.
Substituting this in just gives infinity:
While substituting the parameters into the differential equation before solving it, gives a perfectly finite result:
y[x]/.DSolve[((x (1 - x) y''[x] + (c - (a + b + 1) x) y'[x] - a b y[x])/.subabc) == 0, y[x], x][]
Is there a way to make Mathematica return a valid analytic result that would reduce to the explicit example upon inserting integer parameters?