Conjugate index

<h2 id="properties">Properties</h2>
<p>The following are equivalent characterizations of Hölder conjugates:
</p>
<ul><li>
  
    
      
        
          
            1
            p
          
        
        +
        
          
            1
            q
          
        
        =
        1
        ,
      
    
    {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}=1,}
  
</li>
<li>
  
    
      
        p
        q
        =
        p
        +
        q
        ,
      
    
    {\displaystyle pq=p+q,}
  
</li>
<li>
  
    
      
        
          
            p
            q
          
        
        =
        p
        −
        1
        ,
      
    
    {\displaystyle {\frac {p}{q}}=p-1,}
  
</li>
<li>
  
    
      
        
          
            q
            p
          
        
        =
        q
        −
        1.
      
    
    {\displaystyle {\frac {q}{p}}=q-1.}
  
</li></ul>

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Beatty%2527s_theorem/fteXvhIo">Beatty's theorem</a></li></ul>

<ul><li>Antonevich, A. <i>Linear Functional Equations</i>, Birkhäuser, 1999. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 3-7643-2931-9.</li></ul>
<p><i>This article incorporates material from Conjugate index on <a href="/facts/PlanetMath/wphPCtLf">PlanetMath</a>, which is licensed under the Creative Commons Attribution/Share-Alike License.</i>
</p>

Conjugate index open-in-new

Conjugate index