Just to add, I think they are called "Bessel" filters because of Storch.
H(s) =3D e^(-s) =3D 1/(cosh s + sinh s) =3D (1/sinh s)/( cosh s/sinh s + 1 )
cosh s =3D 1 + s^2/2! + s^4/4! + ... sinh s =3D s + s^3/3! + s^5/5! + ...
Continued fraction expansion of cosh s/sinh s yields:
cosh s/sinh s =3D 1/s + (3/s)||((5/s)||((7/s)||((....
truncating at n=3D3, for example, yields the approximation
cosh s/sinh s ~=3D~ (6s^2 + 15)/(s^3 + 15s)
Adding the numerator and denominator and inserting into the orginal, yields:
H(s) =3D e^(-s) ~=3D~ B_3(s) =3D K/((s^3 + 6s^2 + 15s + 15)
That is the denominator for a bessel LP of order 3. It works the same way for other orders. The polynomials Storch found via this procedure were apparently Bessel type.
Kind of ingenious. I just copied this out of Humpherys. It's in Su, too, Weinburg too, and probably most of them.