# Questions tagged [chebyshev-polynomials]

In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.

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### How to get from Chebyshev to Ihara?

I have competing answers on my question about "Returning Paths on Cubic Graphs Without Backtracking". Assuming Chris is right the following should work. Up to one thing: The number of returning paths ...
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### First kind Chebyshev polynomial to Monomials

Express First kind Chebyshev polynomial in terms of monomials First kind Chebyshev polynomial of order n ($T_n$) is defined in terms of cosine function as follow: 1) $T_n(\cos x)=\cos n x$ ...
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### relation between first kind Chebyshev poly and second kind Chebyshev poly

How do you prove following relation between Chebyshev poly of first kind and Chebyshev poly of second kind: $$dT_n(x)/dx=nU_{n-1}(x)$$
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### How to best approximate higher-degree polynomial in space of lower-degree polynomials?

My question is: Find the best 1-degree approximating polynomial of $f(x)=2x^3+x^2+2x-1$ on $[-1,1]$ in the uniform norm(NOT in the least square sense please)? Orginially, as the title of the post ...
Given a graph $G$ and its adjacency matrix $A$. The $(i,j)$-th element of $A^r$ gives the number of ways to get from vertex $i$ to $j$ in $r$ steps (including backtracking). Now, the number of ...