I have stumbled across something beautiful! I haven’t the time to write of it now, but I can allude to it without fear. Eventually, I will reproduce a very fascinating formula for $latex \pi$.
But first:
Consider the following expression:
$latex \cos \dfrac{\xi}{2} \cos \dfrac{\xi}{4} \cos \dfrac{\xi}{8} … \cos \dfrac{\xi}{2^n}$
It can be simplified into a very simple quotient of $latex sin$ in terms of $latex \xi$.
December 25, 2021 at 4:40 am on Prime rich and prime poorWhat polynomials are allowable for prime-poor polynomials? Could I claim that I have found a better example of a prime-poor polynomial than x^12+488669 by presenting the example (x+3)^12-488601, for example? https://davidlowryduda.com/prime-rich-and-prime-poor/ 
October 19, 2021 at 7:14 pm on An Intuitive Overview of Taylor SeriesHi Bob! The behavior of $c$ is actually quite subtle. It's not true that $c$ is actually a constant. For "nice" functions, what is true is that the mean value $c$ varies continuously over intervals (except at finitely many points). Combined with a form of Darboux's theorem (stating that every function that is the derivative of another function has the ---
October 18, 2021 at 6:09 pm on An Intuitive Overview of Taylor SeriesIt's been a while since there was a comment here, but I'll give it a try in the hope for a response. Your proof gives me a sense of validation in my own work, although I still have questions. I wrote a very similar idea here: https://math.stackexchange.com/q/4277898/225136 . As you can see from a comment that someone left, the proof ---
April 14, 2021 at 3:24 am on Long live opalstack!Thabk you! I was looking for an opinion of a long-term user of Opalstack so your answer was exactly what I needed. April 13, 2021 at 9:32 pm on Long live opalstack!Hi Yavor, I'm very happy with Opalstack. After the initial transition, there have been almost no problems. I'll note that for a few months, opalstack's email setup was rocky, but they figured that out. I'd recommend it. They've been pretty responsive to problems, too. You can see what's troubling people now on their community/support forum: https://community.opalstack.com/. I know a somewhat --- April 13, 2021 at 6:12 pm on Long live opalstack!Hello David, Would you please be so kind to tell us (me) of your (further) experience with Opalstack so far? I myself had to migrate away from WebFaction and I am wondering if now migrating some of my sites to Opalstack is a good idea. Best regards :) 
March 18, 2021 at 5:09 pm on A response to FtYoU’s question on RedditGod bless you David. Great explanation! February 25, 2021 at 6:24 pm on phase_mag_plot: a sage package for plotting complex functionsI'm glad to hear it! I would also read issues or pull requests on github. I think it would not be particularly hard to incorporate this into official sage. I have a local build of sage that includes a variant of phase_mag_plot as the default complex_plot. There are a few additional usability things I need to do before submitting this ---
February 25, 2021 at 5:07 pm on phase_mag_plot: a sage package for plotting complex functionsI took the liberty to download your SageMath module and changed a few options. Since I was not completely clear on the interaction between lightness and color (defined by the argument of the function to be displayed) I decided to weigh these differently. Color, from the colorwheel by 0.8 and lightness by 0.2. I computed the color first and weighed ---
December 23, 2020 at 4:07 pm on Trigonometric and related substitutions in integralsFor Euler substitutions, do you mind explaining the reasoning for the t term in x*sqrt(a) + t. Is there anywhere else I can read up on this? Thanks for this post!
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