The constant problem asks whether an expression involving known constants, integration in finite terms, computation of limits, etc., is equal to zero.
The constant problem, sometimes also called the identity problem (Richardson 1968)
is a very difficult unsolved problem in transcendental number
theory. However, it is known that the problem is undecidable
if the expression involves oscillatory functions such as sine.
However, the Ferguson-Forcade algorithm
is a practical algorithm for determining if there exist integers for given real numbers such that
or else establishing bounds within which no relation can exist (Bailey 1988).
Bailey, D. H. "Numerical Results on the Transcendence of Constants Involving ,
, and Euler's Constant." Math.
Comput.50, 275-281, 1988.Chen, Z.-Z. and Kao, M.-Y. "Reducing
Randomness via Irrational Numbers." 7 Jul 1999. https://arxiv.org/abs/cs/9907011.Chow,
T. Y. "What Is a Closed-Form Number." Amer. Math. Monthly106,
440-448, 1999.Richardson, D. "Some Unsolvable Problems Involving
Elementary Functions of a Real Variable." J. Symbolic Logic33,
514-520, 1968.Richardson, D. "The Elementary Constant Problem."
In Proc. Internat. Symp. on Symbolic and Algebraic Computation, Berkeley, July
27-29, 1992 (Ed. P. S. Wang). ACM Press, 1992.Richardson,
D. "How to Recognize Zero." J. Symb. Comp.24, 627-645, 1997.Sackell,
J. "Zero-Equivalence in Function Fields Defined by Algebraic Differential Equations."
Trans. Amer. Math. Soc.336, 151-171, 1993.
for given real numbers 
such that
,
, and Euler's Constant." Math.
Comput. 50, 275-281, 1988.Chen, Z.-Z. and Kao, M.-Y. "Reducing
Randomness via Irrational Numbers." 7 Jul 1999.