# Tagged Questions

Questions on doubly periodic functions on the complex plane such as Jacobi and Weierstrass elliptic functions.

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### Curious integrals for Jacobi Theta Functions $\int_0^1 \vartheta_n(0,q)dq$

There are various identities for the Jacobi Theta Functions $\vartheta_n(z,q)$ on the MathWorld page and on the Wikipedia page. But I found no integral identities for these functions. Meanwhile, ...
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### jacobi_sn with theta functions and complex argument, test in C++ and wxMaxima

I didn't know whether to ask this in S.O. or here, so if it's the wrong place, I'm sorry. I need an implementation of jacobi_sn in C++ and I chose the equivalent theta functions version (...
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### Elliptic curve, different forms of.

$y^2 = x^3 + mx + c$ An elliptic curve in the form defined in Wikipedia $y^2 = x(x-A)(x+B) = x^3 +(B-A)x^2 + ABx$ Frey's curve has no term in $x^2$, but $2$. does because from Fermat, $A=a^n$ ...
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### “Opposite” point on ellipsis by axis (or vector)

I'm currently working on a little game and am stumped as to how I'd solve this math problem. What I'm trying to do is get the "rotation" needed for B, where B is always opposing A on the Y axis no ...
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### Laurent Series Expansion Logic

Relative to the below image, I am curious about the progression from equation 3.2 to equation 3.3, then from equation 3.3 to equation 3.4. I understand the logic in 3.2. I understand that a Laurent ...
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### Calculating X & Y coordinates of a point that is perpendicular to an ellipse point AND offset by -5

I am trying to calculate an offset point from a point on an ellipse - I need to be perpendicular to each point on the ellipse but 5 points in from the point on the ellipse. The result will probably ...
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### Algebraic equation concerning the Jacobi sn function

What are the solutions $u$ to the equation $\sqrt{1-m} \operatorname{sn} (u \mid \frac{1-m}{1+m}) = 1$ for a given $m$? Because $\mbox{sn}$ is an elliptic function of order 2, we know it attains any ...
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### How to calculate an inner ellipse points that is always a set distance from an outer ellipse points

I have an Ellipse with known coordinates , I would like to know how I can create an inner ellipse coordinates that are exactly 5 inches perpendicular from the outer ellipse points. Please see the ...