# Expansion of hypergeometric function with symbolic parameters

I just tried in Mathematica 11.3

SeriesCoefficient[Hypergeometric2F1[1, 1 - n, 2 + n, w], {w, 0, m}, Assumptions -> n > m > 1 && n \[Element] Integers]


which gives $$\frac{(n+1)! (m-n)!}{(-n)! (m+n+1)!}$$

This cannot be correct, since $$m-n<0$$ and its factorial is infinity. Is there any walkaround for this problem?

• You have negative factorials in the numerator and denominator, so the ratio is regular and equal to $\frac{(-1)^m (n-1)! (n+1)!}{(n-m-1)! (n+m+1)!}$ for $n > m > 1$ and $n$,$m$ integers. – QuantumDot Jan 13 at 15:25

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