mathematica 指数 N 阶导数被视为未知函数 [英] mathematica exponential Nth derivative treated as an unknown function

问题描述

我想创建一个 Hankel 函数列表，根据 N 阶导数定义，但 N 阶导数按照未知函数的导数"下的文档中描述的方式处理，并且未计算.举个例子:

I'd like to create a list of Hankel functions, defined in terms of an Nth derivative, but the Nth order derivatives get treated in the way that is described in the docs under "Derivatives of unknown functions", and left unevaluated. Here's an example:

Clear[x, gaussianExponential]
gaussianExponential[x_] := Exp[- x^2]
FullSimplify[Derivative[2][gaussianExponential[x]]]

我得到:(E^-x^2)^[Prime][Prime]

I get: (E^-x^2)^[Prime][Prime]

(而不是看到求值的导数(并且最终表达式未简化)).

(instead of seeing the derivatives evaluated (and the final expressions are left unsimplified)).

知道这里发生了什么吗?

Any idea what's going on here?

推荐答案

Derivative 适用于函数符号 f，而不适用于在某个点计算的函数 f[x].所以你想要的是

The Derivative applies to the function symbol f, not to the function evaluated at a point f[x]. So what you want is

Clear[x, gaussianExponential]
gaussianExponential[x_] := Exp[-x^2]
Derivative[2][gaussianExponential][x]//FullSimplify

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