First, you can send to multiple email addresses by putting them as arguments to sendmail. That is, a space separated string.

$recipient = "foo@example.com bar@example.com";
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Second, you aren't formatting the email correctly. There must be a blank line between the header and the body.

Third, you should include a To: line in the header with a list of the email addresses being sent to (separated by commas). sendmail will not add the header automatically. If you don't, the mail will show "To: undisclosed-recipients;". And probably be filtered out by spam filters. Sendmail will read the list of addresses from the To: header if you use the "-t" command line switch.