以索引为导数阶的和

Question

I want to define a sum that contains derivatives of a function, where the summation index is the derivative order. Simple example:

x, i = symbols("x i")
f = Function("f")(x)
Sum(diff(f,x,i), [i,1,3])

However, this only returns a sum of zeros. I assume this is because it tries to differentiate f wrt x first, and then wrt i. Since f is not a function of i, it evaluates to zero before it is processed by the Sum function. What I want to happen is

diff(f,x,1)
diff(f,x,2)
diff(f,x,3)

etc.

Is there a way to make this work?

Answer 1

sympy.diff(f,x,i) is equivalent to i 'th order derivative of f only if i is an integer. In your case it is a symbol.

Use instead the builtin sum() along with a generator expression:

>>> sum(diff(f,x,j) for j in range(1,4))
Derivative(f(x), x) + Derivative(f(x), x, x) + Derivative(f(x), x, x, x)