Question: How to get a general expression for derative ?

How to get a general expression here ?



f(s) is the function value  expressed as a integral around s  (singularity)  of a complex function.

f(s) = (int(f(z)/(z-s), z))/(2*Pi*I)

f(s) = -((1/2)*I)*(int(f(z)/(z-s), z))/Pi


f(s) = int(f(z)/(z - s), z)/((2*Pi)*I):


diff(f(s), s) = -((1/2)*I)*(int(f(z)/(z-s)^2, z))/Pi



diff(diff(f(s), s), s) = -((1/2)*I)*(int(2*f(z)/(z-s)^3, z))/Pi


"((ⅆ)^(n))/(ⅆn) f(s)   =  "




quote : "Important consequence.

Above it actually says: "If there is a function f(s) that is somewhere analytic, then you can use such an integral as above to make a new function f '(s), which is also analytic there. And from that a new function f '' and so on.
That means something revolutionary for complex numbers:   "



Question: how to get the "((ⅆ)^(n))/(ⅆn) f(s)  "?

Note : again the form of the answers in Maple : Its not possible to force Maple to come up with this form of answer, ex

``  NULL


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