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戴森猜想


戴森 (Dyson, 1962abc) 基於粒子物理學中的一個問題,猜想 洛朗級數 中的常數項

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

多項式係數

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

威爾遜 (Wilson, 1962) 和 Gunson (1962) 獨立證明了該定理。Good (1970) 隨後發表了一個確鑿的證明。


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麥克唐納常數項猜想, Zeilberger-Bressoud 定理

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參考文獻

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 中被引用

戴森猜想

引用為

Weisstein, Eric W. "戴森猜想。" 來自 --一個 資源。 https://mathworld.tw/DysonsConjecture.html

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