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在 数学 中， 阿培里常数 是一个时常会遇到的 常数 。. 在一些 物理 问题中阿培里常数也会很自然地出现。. 比如说 量子电动力学 里，阿培里常数出现在 电子 的 磁旋比 展开的第二项与第三项中。. 阿培里常数的准确定义是 黎曼ζ函数 的一个值：ζ (3)，. 它的 ...
- 阿培里常数
- 無理數
- .mw-parser-output .serif{font-family:Times,serif}ζ(3)
In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes. That is, it is defined as the number. where ζ is the Riemann zeta function. It has an approximate value of [1] ζ(3) = 1.20205 69031 59594 28539 97381 61511 44999 07649 86292 … (sequence A002117 in the OEIS ). The constant is named after Roger Apéry.
- 1.0011001110111010...
- Irrational
- 1.2020569031595942854...
- ζ(3)
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Apéry's Constant. Download Wolfram Notebook. Apéry's constant is defined by. (1) (OEIS A002117) where is the Riemann zeta function. Apéry (1979) proved that is irrational , although it is not known if it is transcendental . Sorokin (1994) and Nesterenko (1996) subsequently constructed independent proofs for the irrationality of (Hata 2000).
Apéry's theorem. In mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ (3) is irrational. That is, the number. cannot be written as a fraction where p and q are integers. The theorem is named after Roger Apéry . The special values of the Riemann zeta function at even integers ( ) can be shown in ...
2021年4月3日 · \zeta(3) 也被称为Apéry 常数 ，因为Roger Apéry第一个证明了 \zeta(3) 是无理数.所需证的第二个恒等式是由A.A.Markov于1890年首先发现，1953年被Hjortnaes重新发现，1979年被Apéry再次发现并广为宣传。 不过最初的原始论文比较模糊，后续有人重新做过整理
事實上，黎曼ζ函數在偶數上的取值是容易求得的，在奇數上的取值則遠未有一般性成果。這個常數以數學家羅傑·阿培里命名，因為後者在1978年證明了它是一個無理數。 這個結論被稱為阿培里定理。最初的證明很長，而且晦澀難懂，幸好不久後發現了更為簡潔的證明，只需要用到勒讓德多項式。
apery 的词源 [ 1610–20; ape + -ery ] This word is first recorded in the period 1610–20. Other words that entered English at around the same time include: cult , cultivate , institutional , tank , technical -ery is a suffix of nouns denoting occupation, business, calling or condition, place or establishment, goods or products, things ...
