|
In mathematics, at the crossing of number theory and special functions, Apéry's constant is defined as the number : where ζ is the Riemann zeta function. It has an approximate value of〔See .〕 :ζ(3) = . }} Note that this continued fraction is infinite, but it is not known whether this continued fraction is periodic or not. |} This constant 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 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. ==Irrational number== ζ(3) was named ''Apéry's constant'' for the French mathematician Roger Apéry, who proved in 1978 that it is irrational.〔See .〕 This result is known as ''Apéry's theorem''. The original proof is complex and hard to grasp,〔See .〕 and simpler proofs were found later.〔See .〕〔See .〕 It is still not known whether Apéry's constant is transcendental. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Apéry's constant」の詳細全文を読む スポンサード リンク
|