I have numerically verified that the hypergeometric function $_2F_1(a,a;2a;z)$ has no zeros in the unit disc, for a range of real positive $a$ parameters. Is it possible to prove this for all real positive $a$? I found some papers studying the zeros of hypergeometric polynomials, but they are not applicable to my case.
2026-04-12 07:43:16.1775979796
Zeros of hypergeometric function $_2F_1(a,a;2a;z)$ in the unit disc
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