Debye function

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the family of Debye functions is defined by

D
          
            n
          
        
        (
        x
        )
        =
        
          
            n
            
              x
              
                n
              
            
          
        
        
          ∫
          
            0
          
          
            x
          
        
        
          
            
              t
              
                n
              
            
            
              
                e
                
                  t
                
              
              −
              1
            
          
        
        
        d
        t
        .
      
    
    {\displaystyle D_{n}(x)={\frac {n}{x^{n}}}\int _{0}^{x}{\frac {t^{n}}{e^{t}-1}}\,dt.}

The functions are named in honor of <a href="/facts/Peter_Debye/C9rm7nx8">Peter Debye</a>, who came across this function (with n = 3) in 1912 when he analytically computed the <a href="/facts/Heat_capacity/I63nzSyp">heat capacity</a> of what is now called the <a href="/facts/Debye_model/Hak5Spp8">Debye model</a>.

Debye function open-in-new

Debye function