An entire function of order greater than 1 (which means that in some direction it grows faster than a function of exponential type) cannot be of bounded type in any half-plane. We may thus produce a function of bounded type by using an appropriate exponential of "z" and exponentials of arbitrary Nevanlinna functions multiplied by "i", for example:  Concerning the examples given above, the mean type of polynomials or their inverses is zero. The mean type of formula_22 in the upper half-plane is −"a", while in the lower half-plane it is "a". The mean type of formula_45 in both half-planes is 1. Functions of bounded type in the upper half-plane with non-positive mean type and having a continuous, square-integrable extension to the real axis have the interesting property (useful in applications) that the integral (along the real axis)  equals formula_18 if "z" is in the upper half-plane and zero if "z" is in the lower half-plane. This may be termed the Cauchy formula for the upper half-plane.