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The previous post derived the identity and said in a footnote that the identity holds at least forВ x > 1 andВ y > 1. That’s true, but let’s see why the footnote is necessary...
The previous post announced some notes I wrote up based on an article by Henry Baker implementing functions of a complex variable in terms of functions of a real variable. That is,...
В предыдущей части была рассмотрена предыстория комплексных чисел: от их первого открытия до понимания и умения их широко использовать в науке прошли сотни лет. Комплексные числа в...
A couple months ago I wrote about how to compute the sine and cosine of a complex number using only real functions of real variables using the equations You can do something analog...
Let f be an even function with period ПЂ. Then the following remarkable theorem by Lobachevsky holds. This theorem is useful in Fourier analysis and signal processing. It’s useful...
How should we define в€љ(zВІ в€’ 1)? Well, you could square z, subtract 1, and take the square root. What else would you do?! The question turns out to be more subtle than it looks...
There is still active discussion on X about the approximation exp(−x²) ≈ (1 + cos(sin(x) + x))/2 and some are saying this can just be explained by Taylor series: the series fo...
Как создавался этот документ.Это учебное пособие по функциональным уравнениям я не писал руками. Я провёл со студентами ВШЭ онлайн-занятие факультатива по олимпиадной высшей матема...
“You can’t always get what you want. But sometimes you get what you need.” — The Rolling Stones Circular functions and hyperbolic functions aren’t invertible, but we invert them...
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