Gaussian normal distribution curve

[touqra]

I am looking for a mathematical equation which is similar to the Gaussian normal distribution curve, but I need one which terminates at a finite x = X and not at infinity, ie, f(x \geq X) = 0, but, f(x \leq X) =a function which has a Gaussian shape-like curve.
Is there one such as this that you know or in mathematics literatures?

 

[TenaliRaman]

define the Gaussian for any finite interval
f(x)
= gaussian for a<x<b
= 0 otherwise

-- AI

 

[Galileo]

Or consider:
f(x)=Ae^{-x^2}-b
for |x|&lt;\sqrt{\ln(A/b)} and 0 elswhere.
That one is even continuous.

 

[uart]

Or even just a raised cosine, 1 + cos(x) : -pi < x < pi .

 

[touqra]

Is there a mathematical function which is not piece-wise and can be defined for the whole range of x (just by one mathematical relationship)?

 

[matt grime]

Probably not since you are splitting the range up in your own requirements, besides, that is purely a superficial issue for you. If you know what a heaviside function is then, for k some positive real number

H(x+k)(1-H(x-k))f(x)

for some suitably shaped and nomalized function would do and would appear to be a nice single line wouldn't it? Of course

H(y) is defined piecewise.