You can start by reading this link:

http://math.stackexchange.com/questions/454289/how-to-make-any-function-to-repeat-periodically

Thanks Gioacchino de Candia for the reply... Albeit the link you sent was helpful still it has some ambiguity...

By definition there is no Gaussian periodic function, you could use binomial formula which is exactly zero. The natural way is Fourier-expansion - you prescribe the shape and project to Fourier basis. That is how I would do it.

The above comments are true. Bu beyond that I want add something. First I say what purpose it will serve , it is to understand first. So define the  problem .  I think you mean the Co-ordinate geometry-point of view. If it is so take a polar form with proper definition and constraints of the Gaussian curve. Then try to proceed. Thanks.

A periodic Gaussian function seems to be the wrapped normal distribution: http://en.wikipedia.org/wiki/Wrapped_normal_distribution

Hey, thanks everyone for their valuable comments... 

Karthik Soman, my answer clarifies your problem and is the starting point, there is no ambiguity.

George Stoica... Thank you sir...

I am sorry, I cannot answer your question.

With respect Ilmars Kangro

How about the von MIses distribution? It is also known as circular normal distribution which hints at similarities with the gaussian.Following link from wikipedia:

http://en.wikipedia.org/wiki/Von_Mises_distribution

you can use the following function and change the parameters (a, b and c) to fit your data: y=exp(-((a*sin(x)-b)/c).^2)

Hello Karthik Soman , its interesting question. We may approximate Gaussian function using the power-sine or cosine function. We may adjust period by changing sine wave frequency. This is a paper for more details and mathematic formulation: Conference Paper Efficient Approximation of Gaussian Function for Signal and ...

Thanks to Mohamed Kilani , James Foadi , Ilmars Kangro , Gioacchino de Candia Carlos Albuquerque , Sujit Kumar De , Markus Abel and all for Additional Informations