主题
Search

戴森猜想

戴森 (Dyson, 1962abc) 基于粒子物理学中的一个问题，猜想 洛朗级数 中的常数项

product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i)

是多项式系数

((a_1+a_2+...+a_n)!)/(a_1!a_2!...a_n!).

威尔逊 (Wilson, 1962) 和 Gunson (1962) 独立证明了该定理。Good (1970) 随后发表了一个确凿的证明。

另请参阅

麦克唐纳常数项猜想, Zeilberger-Bressoud 定理

使用 Wolfram|Alpha 探索

参考文献

Andrews, G. E. "The Zeilberger-Bressoud Theorem." §4.3 in q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. Providence, RI: Amer. Math. Soc., pp. 36-38, 1986.Dyson, F. "Statistical Theory of the Energy Levels of Complex Systems. I." J. Math. Phys. 3, 140-156, 1962a.Dyson, F. "Statistical Theory of the Energy Levels of Complex Systems. II." J. Math. Phys. 3, 157-165, 1962b.Dyson, F. "Statistical Theory of the Energy Levels of Complex Systems. III." J. Math. Phys. 3, 166-175, 1962c.Good, I. J. "Short Proof of a Conjecture by Dyson." J. Math. Phys. 11, 1884, 1970.Gunson, J. "Proof of a Conjecture of Dyson in the Statistical Theory of Energy Levels." J. Math. Phys. 3, 752-753, 1962.Wilson, K. G. "Proof of a Conjecture by Dyson." J. Math. Phys. 3, 1040-1043, 1962.

在 Wolfram|Alpha 中被引用

戴森猜想

引用为

Weisstein, Eric W. "戴森猜想。" 来自 MathWorld--一个 Wolfram Web 资源。 https://mathworld.net.cn/DysonsConjecture.html

主题分类