Recent content by gty656

I checked for myself in Wolfram some initial values for n and it was ok however I would like to see a full proof with induction being enough for me (When proving the induction step, you will probably need to refer to the definition of recursion except that here we have second-order linear...

Not long ago, I derived the formula for Chebyshev polynomials $$T_{n}\left( x\right)= \sum_{k=0}^{\lfloor \frac{n}{2} \rfloor}{n \choose 2k}x^{n-2k}\left( x^2-1\right)^{k}$$ How to extract the coefficients of this polynomial of degree n ? I tried using Newton's binomial but got a double sum...

My cv has been accepted or not?

Hello I am from Egypt my interests fall into the sciences mainly mathematics and chemistry