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<DIV><SPAN class=630242901-10012021><FONT color=#0000ff size=2
face=Arial>Incidentally, for all you math-heads, the Landen transformation
technique is discussed in Chapter 16, Jacobian Elliptic Functions and Theta
Functions, of the Handbook of Mathematical Functions by Abramowitz and
Stegun (if you like math and you don't have this book, you are missing
out!). Section 16.12 is Descending Landen Transformation (Gauss'
Transformation) (which is what I'm doing), and Section 16.14 is Ascending Landen
Transformation. In the descending form, one ends up with k=0 and
sn = sin. In the ascending form, one ends up with k=1, and sn =
tanh.</FONT></SPAN></DIV>
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face=Arial></FONT></SPAN> </DIV>
<DIV><SPAN class=630242901-10012021><FONT color=#0000ff size=2 face=Arial>So, I
just created an Excel function that calculates the elliptic sine given any angle
and modulus. From that, the poles are calculated directly, in closed
form. The mathematicians were wrong,
Bernie.</FONT></SPAN></DIV></BODY></HTML>