Changes between Initial Version and Version 1 of CarlsonRj


Ignore:
Timestamp:
03/14/11 13:23:17 (4 years ago)
Author:
rtoy
Comment:

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  • CarlsonRj

    v1 v1  
     1= Carlson ''R'',,''j'',, =
     2
     3{{{(carlson-rj x y z p)}}}
     4
     5Carlson'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
     10It is related to the elliptic integral of the third kind by
     11{{{
     12  P(phi,k,n) = integrate((1+n*sin(t)^2)^(-1)*(1-k^2*sin(t)^2)^(-1/2), t, 0, phi)
     13             = sin(phi)*Rf(cos(phi)^2, 1-k^2*sin(phi)^2, 1)
     14                - (n/3)*sin(phi)^3*Rj(cos(phi)^2, 1-k^2*sin(phi)^2, 1, 1+n*sin(phi)^2)
     15}}}
     16
     17Note that Carlson's definition of the integrals has the opposite sign
     18for the parameter ''n'' compared to the definition given by A&S.
     19