function binomialCCDF( n, k, x, y ) {
	var startTerm;
	var result;
	var start;
	var term;
	var i;

	result = pow( x, n );
	if ( result > MIN_VALUE ) {
		term = result;
		for ( i = floor( n - 1 ); i > k; i-- ) {
			term *= ((i + 1) * y) / ((n - i) * x);
			result += term;
		}
	} else {
		// First term underflows so we need to start at the mode of the distribution and work outwards:
		start = floor( n * x );
		if ( start <= k + 1 ) {
			start = floor( k + 2 );
		}
		result = pow( x, start ) * pow( y, n - start );
		result *= binomcoef( floor(n), floor(start) );
		if ( result === 0.0 ) {
			// OK, starting slightly above the mode didn't work, we'll have to sum the terms the old fashioned way:
			for ( i = start - 1; i > k; i-- ) {
				result += pow( x, i ) * pow( y, n - i );
				result *= binomcoef( floor(n), floor(i) );
			}
		} else {
			term = result;
			startTerm = result;
			for ( i = start - 1; i > k; i-- ) {
				term *= ((i + 1) * y) / ((n - i) * x);
				result += term;
			}
			term = startTerm;
			for ( i = start + 1; i <= n; i++ ) {
				term *= (n - i + 1) * x / (i * y);
				result += term;
			}
		}
	}
	return result;
}
For integer arguments we can relate the incomplete beta to the complement of the binomial distribution cdf and use this finite sum.

@private
@param {NonNegativeInteger} n - number of trials
@param {NonNegativeInteger} k - function input
@param {Probability} x - function input
@param {Probability} y - probability equal to `1-x`
@returns {number} sum