Apéry's constant
Sum of the inverses of the positive cubes / From Wikipedia, the free encyclopedia
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In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes. That is, it is defined as the number
Rationality | Irrational |
---|---|
Symbol | ζ(3) |
Representations | |
Decimal | 1.2020569031595942854... |
where ζ is the Riemann zeta function. It has an approximate value of[1]
The constant is named after Roger Apéry. It arises naturally in a number of physical problems, including in the second- and third-order terms of the electron's gyromagnetic ratio using quantum electrodynamics. It also arises in the analysis of random minimum spanning trees[2] and in conjunction with the gamma function when solving certain integrals involving exponential functions in a quotient, which appear occasionally in physics, for instance, when evaluating the two-dimensional case of the Debye model and the Stefan–Boltzmann law.