Already we have defined entire (or integral) function, as those which are analytic in ℂ, and we have noted (C.C.A. Section 9.6) that entire functions which are regular at ∞ are the constant functions, those having a pole at ∞ are the polynomials of degree n ≥ 1, while entire functions with an essential singularity at ∞ are called transcendental entire functions. Elementary example of functions of the last type are the exponential e z , the trigonometric functions sinh z, cos z, and the hyperbolic functions sinh z, cosh z (which are, of course, simple combinations of exponentials).