class_name::class_name (float a, float b){
alpha = a;
beta = b;
}
This is a constructor firstly. Secondly, each constructor is unique to its class. We can do more than simply assigning values in a constructor the way you have asked. The comstructor is a special function, one that initializes variables of a class if required by the coder.
Regarding your question about input parameters, you cannot assign values by simply keeping them the same name. This:
class_name(float alpha, float beta);
Simply defines 2 input parameters in your constructor; it does not assign anything to anything. If your class has a variable named alpha and beta, then it will cause a problem as you have 2 variables with the same name in your function argument. Therefore, this choice is not even valid.
As for your second function, int main() is the function where your program will run. There is only 1 int main() function; you need not declare it anywhere else in your code as it will cause a problem.
As an aside, try finding a good book on the fundamentals of c++, it will assist you in understanding classes in c++ better.