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# Elliptic Theta Functions

All of the elliptic theta functions are functions of two parameters. The second parameter q is the nome and must satisfy {{{|q| < 1}}}.

## Theta 1

(elliptic-theta-1 z q)

First theta function defined by

```  theta1(z, q) = 2*q^(1/4)*sum((-1)^n*q^(n*(n+1))*sin((2*n+1)*z), n, 0, inf)
```

## Theta 2

(elliptic-theta-2 z q)

Second theta function defined by

```  theta2(z, q) = 2*q^(1/4)*sum(q^(n*(n+1))*cos((2*n+1)*z), n, 0, inf)
```

## Theta 3

(elliptic-theta-3 z q)

Third theta function defined by

```  theta3(z, q) = 1 + 2 * sum(q^(n^2)*cos(2*n*z), n, 1, inf)
```

## Theta 4

(elliptic-theta-4 z q)

Fourth theta function defined by

```  theta4(z, q) = 1 + 2*sum((-1)^n*q^(n^2)*cos(2*n*z), n, 1, inf)
```

## Miscellaneous

(elliptic-theta n z q)
Convenience function where n is 1, 2, 3, or 4 for one of the four theta functions
(elliptic-nome m)
Compute the nome q from the parameter m.