In this post, with the help of A-Student, I have proved the two trigonometrical formulae of Euler. In this thread, I will prove 2 more general formlae found in his paper "Subsidium Calculi Sinuum" (Contribution to the calculation of sine) by Euler.
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Ramanujan, the "Euler" of 20th century
The first time I heard of the name Ramanujan was in 2017. At that time, I was wondering on the internet, searching information about i...
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In the previous post, we have successfully derived the power series for $\dfrac{x}{e^x-1}=\displaystyle\sum_{n=0}^{+\infty}\dfrac{B_nx^{n}}...
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I was introduced to the so-called C+iS method when I tried to prove these 2 formulae from the work of Euler. I don't know how to c...
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