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 November 5th, 2019, 03:41 AM #1 Newbie   Joined: Nov 2019 From: Rozebeke, Flanders Posts: 2 Thanks: 0 On process, and on the derivatives of the powers of sine Some background: A few months ago, I was on holiday in Prague. And I saw a nice clock there. Which led me to think about the equation of time. Which led me to think about $\displaystyle y = x + e\,\sin y$ Which led me to think about $\displaystyle \frac{e^k}{k!} \frac{\partial^{k-1}}{\partial x^{k-1}} [\sin^k x]$ Which led me to think about the derivatives of the powers of $\displaystyle \sin$. I had some time there in Prague, waiting for a guided tour to start, so I took out a notebook and played a bit with these notions. I found some nice expressions for the derivatives of the powers of $\displaystyle \sin$. Later I realised that analogue expressions hold for $\displaystyle \cos$, $\displaystyle \sinh$, and $\displaystyle \cosh$. So the past few weekends I took some time to write it all out. And then I did some typesetting in LaTeX. A couple of days ago, I submitted my work to ArXiV and last night it got announced: On the derivatives of the powers of trigonometric and hyperbolic sine and cosine https://arxiv.org/pdf/1911.01386.pdf I know this is not earth-shattering but as far as I can tell, this is original (except for the bit that was already published by Qi (2015), which I properly cited) and I personally find it kind of neat and quite beautiful. Do you agree? Or not? Why? My real question is: Where do I go from here? How do I bring this to the attention of the kind of people who are interested in this kind of thing? Where and how do I invite feedback, both on substance and on presentation? Is anybody helped if I seek to get this published in a peer-reviewed journal? Which one? (How and based on what criteria do I choose a journal?) (Is getting published expensive?)

 Tags derivatives, hyperbolic, powers, process, sine, sine or cosine

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