If , then

Let’s define an analogue of the theta function by replacing that trigonometric cosine with an elliptic , where is the elliptic modulus.

So we’d have:

Here’s a domain colored picture of :

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If , then

Let’s define an analogue of the theta function by replacing that trigonometric cosine with an elliptic , where is the elliptic modulus.

So we’d have:

Here’s a domain colored picture of :

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suppose we have

it looks like this:

since

and

, then there is some number between three and two such that

What my morning’s observation is that if we consider something like:

So,: