 Such functions are sometimes called self-conjugate (the conjugate function, formula_4, being given by formula_5

If the real part of an entire function is known in a neighborhood of a point then both the real and imaginary parts are known for the whole complex plane, up to an imaginary constant.For instance, if the real part is known in a neighborhood of zero, then we can find the coefficients for "n" > 0 from the following derivatives with respect to a real variable "r"