What are...Chebyshev polynomials? скачать в хорошем качестве

What are...Chebyshev polynomials?

Goal. I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much. This time. What are...Chebyshev polynomials? Or: Fibonacci with signs? Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Slides. http://www.dtubbenhauer.com/youtube.html Chebyshev polynomials. https://en.wikipedia.org/wiki/Chebysh... The normalization I use is U_n(x)=U’_{n+1}(x/2), where U’ is the one from wikipedia. Fibonacci polynomials. https://en.wikipedia.org/wiki/Fibonac... First and second kind in OEIS. https://oeis.org/A028297 https://oeis.org/A053117 Fibonacci and Chebyshev. https://www.jstor.org/stable/30037546 http://www.physics.utah.edu/~lebohec/... Kronecker’s theorem. https://math.stackexchange.com/questi... https://www.jstor.org/stable/1970656 Runge and Chebyshev. https://en.wikipedia.org/wiki/Chebysh... https://en.wikipedia.org/wiki/Runge%2... (Stone-)Weierstrass approximation. https://en.wikipedia.org/wiki/Stone%E... Mathematica. https://mathematica.stackexchange.com... https://demonstrations.wolfram.com/Ch... https://demonstrations.wolfram.com/Ru... https://demonstrations.wolfram.com/Co... https://demonstrations.wolfram.com/Po... https://reference.wolfram.com/languag... https://reference.wolfram.com/languag... Pictures used. https://en.wikipedia.org/wiki/Fibonac... Screenshots from https://demonstrations.wolfram.com/Ru...