About: Hypertranscendental number

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A complex number is said to be hypertranscendental if it is not the value at an of a function which is the solution of an algebraic differential equation with coefficients in Z[r] and with algebraic initial conditions. The term was introduced by D. D. Morduhai-Boltovskoi in "Hypertranscendental numbers and hypertranscendental functions" (1949). Any hypertranscendental number is also a transcendental number.

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  • A complex number is said to be hypertranscendental if it is not the value at an of a function which is the solution of an algebraic differential equation with coefficients in Z[r] and with algebraic initial conditions. The term was introduced by D. D. Morduhai-Boltovskoi in "Hypertranscendental numbers and hypertranscendental functions" (1949). 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 . Any hypertranscendental number is also a transcendental number. (en)
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  • A complex number is said to be hypertranscendental if it is not the value at an of a function which is the solution of an algebraic differential equation with coefficients in Z[r] and with algebraic initial conditions. The term was introduced by D. D. Morduhai-Boltovskoi in "Hypertranscendental numbers and hypertranscendental functions" (1949). Any hypertranscendental number is also a transcendental number. (en)
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  • Hypertranscendental number (en)
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