When calculating a Partition function, I encounter the following summation $$\sum_{n=0}^{\infty} x^n q^{n^2}.$$ I know that the sum$\sum_{n=-\infty}^{\infty} x^n q^{n^2}$ is a Theta function , but I do not know how to perform the sum from 0

Can anyone help?

(By the way I would like to have the result in an infinite product form, which I can easily do in the Theta case using Jacobi's triple product identity)


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