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The argument of the complete elliptic integrals is m=k^2, not k.

• To: mathgroup at yoda.ncsa.uiuc.edu
• Subject: The argument of the complete elliptic integrals is m=k^2, not k.
• From: blachman%gtewd.dnet at gte.com (NELSON M. BLACHMAN)
• Date: Fri, 9 Aug 91 16:21:22 -0400

  After spending a couple of days trying to figure out why I was getting 
impossible results from some Mma 1.2 MS-DOS 386/7 calculations involving the 
complete elliptic integrals  E(k)  and  K(k),  I discovered that the  m  given 
by Mma help as the argument of  EllipticE[m]  is actually the square of the  
k  that serves in many books as the argument of these functions.  Thus, I had 
to change my  EllipticE[k]  to  EllipticE[k^2]  and my  EllipticK[k]  to  
EllipticK[k^2].  The heading of Mma help's definition of  EllipticK[k]  needs 
to be changed to  EllipticK[m],  and  m  needs to be defined in both 
definitions as  k^2.  

  Mma's use of  K(m)  as the definition of  EllipticK[k]  should have alerted 
me more quickly to the problem!   It would also have helped if Mma had been 
able to exhibit a couple of terms of the (Hypergeometric2F1) power series for 
its  E(m)  and  K(m)  around  m = 0.  

					Nelson M. Blachman
					GTE Government Systems Corp.
					Mountain View, California
					blachman%gtewd.dnet at bunny.gte.com