Problem :- 
we have successfully managed to add event to google calendar through php api client, but what i want is to make that event repeat every year , such as company anniversary etc, i didn’t find that in the google documentation also ,so what should be added while creating event for repetitions.

Solution:- 
There is documentation for recurring event

$event = new Google_Service_Calendar_Event();
$event->setSummary('Appointment');
$event->setLocation('Somewhere');
$start = new Google_Service_Calendar_EventDateTime();
$start->setDateTime('2011-06-03T10:00:00.000-07:00');
$start->setTimeZone('America/Los_Angeles');
$event->setStart($start);
$end = new Google_Service_Calendar_EventDateTime();
$end->setDateTime('2011-06-03T10:25:00.000-07:00');
$end->setTimeZone('America/Los_Angeles');
$event->setEnd($end);
$event->setRecurrence(array('RRULE:FREQ=YEARLY;UNTIL=20110701T170000Z'));
$attendee1 = new Google_Service_Calendar_EventAttendee();
$attendee1->setEmail('attendeeEmail');
// ...
$attendees = array($attendee1,
                   // ...
                   );
$event->attendees = $attendees;
$recurringEvent = $service->events->insert('primary', $event);

echo $recurringEvent->getId();