The symmetric derivative looks like there’s an average in it, so what about changing that average

with something else, like the arithmetic geometric mean:

# agm-ized symmetric derivative

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The symmetric derivative looks like there’s an average in it, so what about changing that average

with something else, like the arithmetic geometric mean:

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Made with GAP

I’m going to try to put up an uncompressed version somewhere -the file weighs in at 900mb, but it’s interesting.

Set , then the sum:

can be interpreted as the value of the Laplace

Transform of at :

First, I’ve rendered a 1024×1024 video of the Newton’s Method of the third Jacobi theta function ϑ3(z,q), for |q| = 0.90190165617299947 or thereabouts. This piece is entitled *The Swift Luminescent Energy Drink of the Psyche, or When Goorialla Whirls and Whorls and Roars*

Secondly, using GAP, I’ve made a video of all Cayley tables of finite groups of order 128:

And finally, A video showing Klein’s j-invariant under the transformation in :