# How can I remove vanishing derivatives of hypergeometric functions?

I have a lot of expressions containing derivatives of hypergeometric functions of the sort:

$$_2F_1^{(0,0,1,0)} \left(\frac{1}{2} , 1 ; \frac{3}{2} ; 0 \right). \tag{1}$$

The last argument is always $$0$$. This is not evaluated, but if I used N then it evaluates to $$0$$. How can such expressions consistently be removed from my expressions?

Consider the following example (sorry I do not know how to properly format the hypergeometric function in the code environment, it's just copy-paste):

15 g^2 f[1] \[CapitalDelta]c[1] - 30 g^2 f[1] \[CapitalDelta]c[1] \!$$\*SuperscriptBox[\(Hypergeometric2F1$$, TagBox[RowBox[{"(", RowBox[{"0", ",", "0", ",", "1", ",", "0"}], ")"}], Derivative], MultilineFunction->None]\)[1/2, 2, 5/2, 0]


The second term evaluates to $$0$$ with N. I can use /.{... -> N[...]} but since I have a lot of functions it would be better to use something else.

• @BobHanlon Thanks, but what if I have other hypergeometric functions which vanish, for example Derivative[1, 0, 0, 0]Hypergeometric2F1][1/2, 1, 5/2, 0]?
– Pxx
Jul 28, 2020 at 15:29
– Pxx
Jul 28, 2020 at 20:51

Use ReplaceAll to replace expressions that numerically evaluate to zero with zero.
Clear["Global*"]
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