How to specify an HTML element in the page to generate PDF document using tcpdf PHP library and using jquery and ajax

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I am using tcpdf php library to generate pdf documents. I need to specify an html element in the page to generate pdf document using jQuery and ajax. Here is ajax_test.php code:

$pdf = new TCPDF();
$pdf->setPrintHeader(false);
$pdf->setPrintFooter(false);
$pdf->AddPage();
//$pdf->Cell(190, 10, 'Hello world!', 1, 1, 'C');
$pdf->Output();

Now this is table.php code:

<h2>HTML Table</h2>
<p>Hello world!</p>
<table>
  <tr>
    <th>Company</th>
    <th>Contact</th>
    <th>Country</th>
  </tr>
  <tr>
    <td>Alfreds Futterkiste</td>
    <td>Maria Anders</td>
    <td>Germany</td>
  </tr>
  <tr>
    <td>Centro comercial Moctezuma</td>
    <td>Francisco Chang</td>
    <td>Mexico</td>
  </tr>
  <tr>
    <td>Ernst Handel</td>
    <td>Roland Mendel</td>
    <td>Austria</td>
  </tr>
  <tr>
    <td>Island Trading</td>
    <td>Helen Bennett</td>
    <td>UK</td>
  </tr>
  <tr>
    <td>Laughing Bacchus Winecellars</td>
    <td>Yoshi Tannamuri</td>
    <td>Canada</td>
  </tr>
  <tr>
    <td>Magazzini Alimentari Riuniti</td>
    <td>Giovanni Rovelli</td>
    <td>Italy</td>
  </tr>
</table>
<button>PDF</button>

I need when I press the pdf button download ONLY the table without refreshing the page using jQuery and ajax.

What I have tried:

How can I do this? Is there a way of doing this?