A hypertranscendental function is a function which is not the solution of an algebraic differential equation with coefficients in Z (the integers) and with algebraic initial conditions. The term was introduced by Mordukhai-Boltovski in "Hypertranscendental numbers and hypertranscendental functions" (1949). Hypertranscendental functions usually arise as the solutions to functional equations, for example the Gamma function.In mathematics, a function is a relation between a given set of elements called the domain and a set of elements called the codomain. The function associates each element in the domain with exactly one element in the codomain. The elements so related can be any kind of thing (words, objects, qualities) but are typically mathematical quantities, such as real numbers.

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