What is a two-sided geometric distribution?

I found in some articles (such as this) references to two-sided geometric distribution. But I went through texts of probability and did not find anything called "two-sided geometric distribution". What does this mean? And where can I find standard formulas for this model?

• Probably this is the distribution with density $ce^{-k|x|}$. – Alexandre Eremenko Aug 7 '15 at 13:45
• @Alexandre Eremenko: On the integers, that is. As a density (on the reals) it is called the double exponential distribution. – kjetil b halvorsen Aug 7 '15 at 13:56
• @AlexandreEremenko How is this related to the standard geometric distribution? Could you refer me to some text on this subject? A simple internet search did not reveal much. Thanks a lot. – Arani Aug 7 '15 at 15:30
• @AlexandreEremenko Also, the text says that its density is $\frac{\alpha - 1}{\alpha + 1} \alpha^{-|k|}$. I am not sure how this follows from the above function. – Arani Aug 7 '15 at 15:36