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 Timestamp:

03/14/11 13:23:17 (4 years ago)
 Author:

rtoy
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v1


 1  = Carlson ''R'',,''j'',, = 
 2  
 3  {{{(carlsonrj x y z p)}}} 
 4  
 5  Carlson's ''R'',,''j'',, is defined by 
 6  {{{ 
 7  Rj(x,y,z,p) = integrate(3/2*(t+x)^(1/2)*(t+y)^(1/2)*(t+z)^(1/2)*(t+p)^(1), t, 0, inf) 
 8  }}} 
 9  
 10  It is related to the elliptic integral of the third kind by 
 11  {{{ 
 12  P(phi,k,n) = integrate((1+n*sin(t)^2)^(1)*(1k^2*sin(t)^2)^(1/2), t, 0, phi) 
 13  = sin(phi)*Rf(cos(phi)^2, 1k^2*sin(phi)^2, 1) 
 14   (n/3)*sin(phi)^3*Rj(cos(phi)^2, 1k^2*sin(phi)^2, 1, 1+n*sin(phi)^2) 
 15  }}} 
 16  
 17  Note that Carlson's definition of the integrals has the opposite sign 
 18  for the parameter ''n'' compared to the definition given by A&S. 
 19  