theta in zeta

Let \phi=(1+\sqrt{5})/2, then consider
V(z)=\sum_{n=1}^{\infty} \frac{\theta_{1}(z, e^{-\pi\phi n})}{n^{z}}

Remarks on V(z):
It is reminiscent of a Clausen function, but I have, a la “The Jacobi theta functions are the elliptic analogs of the exponential function”, replaced the trigonmetric function with a Jacobi theta function. I see that there are some references to “q-Clausen functions”, but I can’t get at them. So have some domain colored pictures, which may or may not be accurate:


Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s