Hi,
As I understand, you want to sync SharePoint calendar with the SharePoint calendar list in Outlook by client side code
in SharePoint 2013.
Why don’t you use the “connect to outlook” button in the ribbon? It will sync the SharePoint calendar list with the calendar in outlook.
If you use the JavaScript code, it cannot get some information from client side.
In the article below all events in calendar will be showed in Google Calendar or Outlook calendar by getting SMTP outgoing mail server name in SharePoint. For more detailed information, you could refer to the article below.
The article below is about deliver meeting request from SharePoint Calendar programmatically. It also can work in SharePoint 2013.
https://nhutcmos.wordpress.com/2010/12/28/deliver-meeting-request-from-sharepoint-calendar-programmatically/
More references:
The article below is about how to: Synchronize Outlook with a SharePoint Folder.
https://msdn.microsoft.com/en-us/library/office/ff424483(v=office.15).aspx
The article below is about SharePoint calendars II: Connect a SharePoint calendar to Outlook.
https://support.office.com/en-us/article/SharePoint-calendars-II-Connect-a-SharePoint-calendar-to-Outlook-fbcc144e-d984-45a7-ad7b-6bca33a4561d
Best regards,
Sara Fan
TechNet Community Support
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