Merge sort algorithm in javascript

MergeSort.js

var merge_sort = function(array, b, e){
	
    if(b < e) {
        var m = Math.floor((b + e) / 2);
	//Recursive stuff
	merge_sort(array, b, m);
	merge_sort(array, m+1, e);
	//Merge stuff
	var lower = [],
        higher = [];
        
        var i = 0,
	    j = 0,
            k = b;

	for( ; k <= m; k++, i++)
            lower[i] = array[k];

	for( ; k <= e; k++, j++)
	    higher[j] = array[k];
		
	i = 0;
	j = 0;
	k = b;

	while(i < lower.length && j < higher.length){
            if(lower[i] < higher[j])
	        array[k++] = lower[i++];
	    else
	        array[k++] = higher[j++];
	}		

	while(i < lower.length)
	    array[k++] = lower[i++];

	while(j < higher.lenth)
	    array[k++] = higher[j++];
    }
};