Chebyshev rational functions

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Chebyshev rational functions are a sequence of functions which are both <a href="/facts/Rational_functions/2nJGu0Ko">rational</a> and <a href="/facts/Orthogonal_functions/2MmN826Q">orthogonal</a>. They are named after <a href="/facts/Pafnuty_Chebyshev/LzRqLqRm">Pafnuty Chebyshev</a>. A rational Chebyshev function of degree n is defined as:

R
          
            n
          
        
        (
        x
        )
         
        
          
            
              
                =
              
              
                
                  d
                  e
                  f
                
              
            
          
        
         
        
          T
          
            n
          
        
        
          (
          
            
              
                x
                −
                1
              
              
                x
                +
                1
              
            
          
          )
        
      
    
    {\displaystyle R_{n}(x)\ {\stackrel {\mathrm {def} }{=}}\ T_{n}\left({\frac {x-1}{x+1}}\right)}

where Tn(x) is a <a href="/facts/Chebyshev_polynomial/HoBINqgC">Chebyshev polynomial</a> of the first kind.

Chebyshev rational functions open-in-new

Chebyshev rational functions