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I have a hypergeometric function. When I plot it, the plotted value at $a=110$ doesn't match the value I get from direct evaluation.

Plot[Hypergeometric2F1[1 + a, 1 - a, 52, .9], {a, 100, 110}]  

From the plot, for $a=110$, I got the value of hypergeometric function is $-4.12\times 10^{-7}$. But when I try to find out by direct evaluation of

Hypergeometric2F1[1 + a, 1 - a, 5/2, .9] /. a -> 110  

I get $1.7867 \times 10^{15}$.

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You don't have a plotting problem, you have a numerics problem. Machine arithematic isn't good enough to get an accurate value for

Hypergeometric2F1[1 + a, 1 - a, 5/2, .9] /. a -> 110

but you are forcing the computation to be made with machine arithmetic by giving .9 as the 4th argument. However, if you substitute 9/10 for .9, you will get a result consistent with your plot.

Hypergeometric2F1[1 + a, 1 - a, 5/2, 9/10] /. a -> 110 // N

6.72304*10^-6

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    $\begingroup$ The OP could also use arbitrary precision, e.g., Hypergeometric2F1[1 + a, 1 - a, 5/2, 0.9`20] /. a->110 $\endgroup$ – Bob Hanlon Dec 16 '17 at 18:21

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