[sdiy] 90-degree phase displacement network calculations

[Ian Fritz]

I've used "A Course of Modern Analysis" by Whittaker and Watson for 
advanced math topics. It, too, covers the Landen Transformation in the 
Theta Function and Jacobian Elliptical Functions chapters. I was 
surprised to see that I had some scribbling in the margins, so I must 
have gone through all this before at some point!

Ian


On 1/9/2021 6:38 PM, David G Dixon wrote:
> 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.
> 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.
> 
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ijfritz.byethost4.com