Does anybody know how to obtain the z->1 expansion for the Gauss Hypergeometric 2F1(a,b;c;z) on Mathematica as shown here ? I tried to use Series with the assumption c-a-b non-integer, but the result is given in terms of Floor, Ceiling... I would like to have a result in terms of the Gamma functions, if possible, or other nice functions. I tried following the answer with FunctionExpand and the one with Inactive[Sum] given here , but with no success.


  • $\begingroup$ Try: Series[Hypergeometric2F1[a, b, c, z], {z, 1, 1}, Assumptions -> {z == 1, -a - b + c > 0}] $\endgroup$ Mar 11, 2021 at 14:23
  • $\begingroup$ @MariuszIwaniuk The assumption z==1 seems to be unnecessary for an expansion near z~1 I think. $\endgroup$ Mar 11, 2021 at 15:01


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