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Tagged with combinatorial-identities cv.complex-variables
3 questions
7
votes
1
answer
256
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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 ...
1
vote
1
answer
179
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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 ...
2
votes
0
answers
153
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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|^...