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单词 Constant Problem
释义

Constant Problem

Given an expression involving known constants, integration in finite terms, computation of limits, etc., determine if theexpression is equal to Zero. The constant problem is a very difficult unsolved problem in TranscendentalNumber theory. However, it is known that the problem is Undecidable if the expression involves oscillatoryfunctions such as Sine. However, the Ferguson-Forcade Algorithm is a practical algorithm for determining ifthere exist integers for given real numbers such that


or else establish bounds within which no relation can exist (Bailey 1988).

See also Ferguson-Forcade Algorithm, Integer Relation, Schanuel's Conjecture


References

Bailey, D. H. ``Numerical Results on the Transcendence of Constants Involving , , and Euler's Constant.'' Math. Comput. 50, 275-281, 1988.

Sackell, J. ``Zero-Equivalence in Function Fields Defined by Algebraic Differential Equations.'' Trans. Amer. Math. Soc. 336, 151-171, 1993.


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