f[n_, x_] := 
      b^n x^n (Pi - x)^
            n/n!

f[n, x]

F[n_, x_] := 
      Sum[(-1)^i D[f[n, x], {x, 2  i}], {i, 0, n}]

F[10, x]

F[10, x] /. x -> 0

F[4, x] /. x -> Pi

F[10, x] /. 
        x -> 0//N

F[30, x] /. x -> 0

N[F[30, x] /. x -> 0, 100]

D[F[6, x], {x, 2}] + F[6, x]  -  f[6, x]

f[n, x] /. Pi -> a/b