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If you only want to use the tabulated values, then linear interpolation using the table can be done in the way explained in heropup 's answer. In this case it doesn't make sense to go beyond linear interpolation. But in general, you can use Newton's method, which you can derive as follows. We define the difference operator $\Delta$ that acts on the tabulated function $\Phi(x)$ as $\Delta\Phi(x ...
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