Hypertranscendental number

A complex number is said to be hypertranscendental if it is not the value at an algebraic point of a function which is the solution of an algebraic differential equation with coefficients in $\backslash mathbb\{Z\}[r]$ and with algebraic initial conditions.

The term was introduced by D. D. Morduhai-Boltovskoi in "Hypertranscendental numbers and hypertranscendental functions" (1949).{{Cite journal |last=Mordukhai-Boltovskoi |first=Dmitrii Dmitrievich |date=1949 |title=Hypertranscendental numbers and hypertranscendental functions |journal=Doklady Akademii Nauk SSSR |volume=64 |pages=21–24}}

The term is related to transcendental numbers, which are numbers which are not a solution of a non-zero polynomial equation with rational coefficients. The number $e$ is transcendental but not hypertranscendental, as it can be generated from the solution to the differential equation $y\text{'}\; =\; y$.

Any hypertranscendental number is also a transcendental number.