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Mathematics
General Math
Can chatgpt accurately calculate expected lengths in Pascal's triangle?
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[QUOTE="Infrared, post: 6845426, member: 467682"] Aside from the fact that ##\varphi## is not uniquely defined given ##e^{i\varphi}##, still no. Your function is always real with nonconstant real part, so it can't possibly satisfy the Cauchy-Riemann equations. Since every harmonic function is the real (or in this case imaginary) part of a holomorphic function, your question should be equivalent to asking whether there is a nonconstant harmonic function vanishing on your curve. Google finds me a paper considering exactly this question: [URL]https://www.ams.org/journals/tran/1966-123-02/S0002-9947-1966-0197755-5/S0002-9947-1966-0197755-5.pdf[/URL] In particular, if you go to section III.2, they show that it is possible for a parabola. [/QUOTE]
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Can chatgpt accurately calculate expected lengths in Pascal's triangle?
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