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7 votes
1 answer
256 views

Reference for permanent integral identity

$\DeclareMathOperator\perm{perm}\DeclareMathOperator\diag{diag}$Using MacMahon's master theorem, the properties of complex gaussian integrals, and Cauchy's integral theorem one can show that the ...
motherboard's user avatar
1 vote
1 answer
179 views

One trig "survives" a binomial summation: why?

I've seen many trigonometric identities but here is one that I encountered for which I did not find a reference. In case you wonder where this came from, I was investigating certain $q$-series in ...
T. Amdeberhan's user avatar
2 votes
0 answers
153 views

system of complex number equations

Let $a_1,a_2,a_3,a_4\in \mathbb{C}$ be distinct such that $$a_1^3+a_2^3+a_3^3+a_4^3=0$$ $$(1+|a_1|^2)a_1^2+(1+|a_2|^2)a_2^2+(1+|a_3|^2)a_3^2+(1+|a_4|^2)a_4^2=0$$ $$(1+2|a_1|^2+2|a_1|^4)a_1+(1+2|a_2|^...
Ma Na's user avatar
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