This is a check (up to the 7th derivative) that shows that the massive field wipes out the odd derivatives that contribute to the Euler-Maclaurin sum used to calculate the magnitude of the Casimir effect.  Hw1 problem V.

$Assumptions = b > 0;
ClearAll[fp, fpp]
fp = -2 n Sqrt[n^2 + b^2] f[ (Pi/a) Sqrt[ n^2 + b^2]]
fpp = D[fp, n]
f3p = D[fpp, n]

f4p = D[f3p, n];
f5p = D[f4p, n];
f6p = D[f5p, n];
f7p = D[f6p, n];

fp/. n -> 0
fpp/. n -> 0 // Simplify
f3p/. n -> 0
f4p/. n -> 0 // Simplify
f5p/. n -> 0
f6p/. n -> 0 // Simplify
f7p/. n -> 0