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7

Update: I think this is a numeric precision problem rather than a matter of the behavior of Re. I don't know if I should leave my original answer below for reference or remove it. Consider: expr = MathieuC[MathieuCharacteristicA[-(19999999999/10000000000), -2], -2, 5]; N[expr] N[expr, 15] SetPrecision[expr, 15] -9.85323*10^-16 + 3.39211*10^-8 I ...

6

I think your problems are made by order of appling Re and N. Re@Bloch is not yet a state before the computation. So you have to apply the computation by Re@Norder. Block[{$MaxExtraPrecision = 500, ϵ = 10^-10}, Re@N@BlochΚ[-2 + ϵ, -1, -10]] Block[{$MaxExtraPrecision = 1000, ϵ = 10^-20}, Re@N@BlochΚ[-2 + ϵ, -1, -10]] Block[{\$MaxExtraPrecision = 500, ϵ = ...

2

Using N on exact input avoids the round-off error from calculating the two hypergeometric functions separately. (I stopped before x = 1, since that produces a divide-by-zero error.) ListLinePlot@ N@Table[Hypergeometric2F1Regularized[601, Rationalize[100.1], 100, x] / Hypergeometric2F1Regularized[600, Rationalize[100.1], 100, x], {x, 0, 1 - ...

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