Are you trying to say that you have a general formula for a Low Pass filter and you do not know how to solve an equation so that you can have the numerical values you need for that low pass filter to let through only the [0->fm) specific bandwidth you have in mind?
I think we really can't understand your question very well, try to explain it in more words and phrases...
For examples of filters where you only need to input parameters, you can use "fdatool" in Matlab, the grasphycal interface should help a little, even though you do not see formulas direcftly, you can get ideas ...