What is this quotient of partial derivatives of the first Jacobi's Theta function

Let $\theta_1(x,\tau)$ be the first Jacobi's theta function: $$\theta_1(x)=\theta_1(x,\tau)=-i \sum_{n\in \mathbb Z} (-1)^{n}e^{i \pi (n+1/2)^2\tau}e^{2i\pi(n+1/2)x}\qquad x\in \mathbb C, \, \tau\in \mathbb H=\{ z \, \lvert {\rm Im}(z)>0\, \}$$

Let ' denotes the differentiation with respect to the variable $x$ and let's write $\theta'=\theta_1'(0,\tau), \theta''=\theta_1''(0,\tau)$, etc…

Let's consider the following function of the variable $\tau$: $$\mu: \mathbb H\rightarrow \mathbb C\, , \; \tau \mapsto \frac{1}{3}\frac{\theta'''}{\theta'}\, .$$

Is this function already known? If yes, some references would be welcome.

Thanks.

• What "is this indeed the case"?? That the function is well known or what? – Timbuc Nov 4 '14 at 16:54
• @Timbuc: question edited. – ElBabak Nov 4 '14 at 19:44