Jacobi Theta Functions
Let $x$ be a real number and $q$ a positive real number with $0 < q < 1$, this calculator evaluates the following four functions.
- Jacobi theta 1 function \[\theta_1(x,q)=2\sum_{n=0}^\infty (-1)^n q^{\left(n+\frac{1}{2}\right)^2}\sin((2n+1)x)\]
- Jacobi theta 2 function \[\theta_2(x,q)=2\sum_{n=0}^\infty q^{\left(n+\frac{1}{2}\right)^2}\cos((2n+1)x)\]
- Jacobi theta 3 function \[\theta_3(x,q)=1+2\sum_{n=1}^\infty q^{n^2}\cos(2nx)\]
- Jacobi theta 4 function \[\theta_4(x,q)=1+2\sum_{n=1}^\infty (-1)^n q^{n^2}\cos(2nx)\]