Unable to initialize a customized jQuery calendar

I am trying to implement a jquery range calendar to an existing project, but I am unable to make the calendar code to work in my project.

Here is the code for the calendar.

If I put this .js file as it is in my project, I get a "jQuery is not defined error", therefore is surronded the code with a function looking like this :

function initializeRangeCalendar($, window, undefined) {

    $.fn.rangeCalendar = function(options) {

    ...
}

Then I am initializing the function in one of my .ashx files in this way : string init = "var init = function() { " + "initJUI();" + "if (typeof initializeRangeCalendar == 'function' ) { initializeRangeCalendar(jQuery, window); } ;" + ....

Then, when I eventually try to call the calendar on my page I get a bunch of errors indicating that the calendar functions and variables are not defined.

Can anyone help me make this work?