@@jeromejean-charles6163 Thanks for the positive feedback. I always try to motivate my videos with some question- I do think that the great mathematicians who made all these discoveries were trying to answer specific questions. It helps us understand how these great mathematical discoveries came about. Thanks again.
Euler's proof of the Basel problem in Introduction to the Analysis of the Infinities is really fun, as is the rest of this book. See the Euler Archive. There is an English translation, which I belive is still in print.
The coefficients in front of the derivatives of f(x) in the formula of S'(x) are clearly values of the Zeta function at negative integers (and at zero). Has this been proven rigorously?
@@eiseks3410 Thanks for your question. You are absolutely correct in observing that the Bernoulli numbers are very closely related to values of the zeta function. I have a video coming up about this. Stay tuned!
@@nin10dorox I’m glad you enjoyed the video. Here are a couple sources that you might find helpful if you want to see Euler’s original argument: arxiv.org/pdf/0806.4096 And: www.ms.uky.edu/~sohum/ma330/files/euler_zeta_ayoub.pdf
First, and phenomenal vid i especially like the derivation vids 🫡
Thanks so much for the positive feedback! I’m glad you enjoyed the video.
At 4mm.30 So great to give a motivating question thank you.
@@jeromejean-charles6163 Thanks for the positive feedback. I always try to motivate my videos with some question- I do think that the great mathematicians who made all these discoveries were trying to answer specific questions. It helps us understand how these great mathematical discoveries came about. Thanks again.
Euler's proof of the Basel problem in Introduction to the Analysis of the Infinities is really fun, as is the rest of this book. See the Euler Archive. There is an English translation, which I belive is still in print.
@@Calcprof Thanks. I’ll be doing a video about that soon!
The coefficients in front of the derivatives of f(x) in the formula of S'(x) are clearly values of the Zeta function at negative integers (and at zero). Has this been proven rigorously?
@@eiseks3410 Thanks for your question. You are absolutely correct in observing that the Bernoulli numbers are very closely related to values of the zeta function. I have a video coming up about this. Stay tuned!
This is great! Do you have a source linking this derivation to Euler? I've been having trouble finding any papers laying out his method.
@@nin10dorox I’m glad you enjoyed the video. Here are a couple sources that you might find helpful if you want to see Euler’s original argument:
arxiv.org/pdf/0806.4096
And:
www.ms.uky.edu/~sohum/ma330/files/euler_zeta_ayoub.pdf