I have a DataTable that I'm bringing data in via ajax like such:

<script>
        $(document).ready(function () {
            $(LogTable).DataTable({
                serverSide: true,
                ajax: {
                    url: "/Log/GetAllLogData",
                    type: "POST",
                    dataType: "json"
                },
                columns: [
                    { "data": "Id", "name": "Id" },
                    { "data": "SampleType", "name": "SampleType" },
                    { "data": "Value", "name": "Value" },
                    { "data": "Program", "name": "Program" },
                    { "data": "QC", "name": "QC" },
                    { "data": "Comments", "name": "Comments" },
                    { "data": "DateAssigned", name: "Date Assigned" },
                    { "data": "CheckedInDate", "name": "CheckedInDate" },
                    { "data": "Discarded", "name": "Discarded"},
                    ],
                processing: true,
                dom: "ftir",
                scrollY: 600,
                scroller: { displayBuffer: 50 },
                order: [[0, 'desc']],
                pageLength: 1000,
                columnDefs: [{
                    targets: 'no-sort',
                    orderable: false
                }]
            });
        });
    </script>

Previously before using Ajax and using a smaller recordset I would have two buttons at the end of the table, one for Edit and one for Delete. The Edit button is a Ajax.BeginForm that will bring up a modal with the selected record. The delete just brings up an alert but still uses Ajax.BeginForm. Before I would format the buttons just in a separate <td> and add the Ajax.BeginForm into the <td> directly like so:

 @if (edit)
        {
            <td class="no-click">
                @using (Ajax.BeginForm(actionName: "LogModal", routeValues: new { id = log.Id }, htmlAttributes: null, ajaxOptions: new AjaxOptions
                {
                    InsertionMode = insertionMode,
                    UpdateTargetId = LogContent,
                    OnSuccess = success,
                    OnFailure = fail,
                    LoadingElementId = ajax
                }))
                {
                   @Html.AntiForgeryToken()
                   <button class="link-button text-info" type="submit"><span class="glyphicon glyphicon-pencil"></span></button>
                }
            </td>
        }
@if (remove)
        {
            <td class="no-click">
                @using (Ajax.BeginForm(actionName: "RemoveLog", routeValues: new { id = log.Id }, htmlAttributes: null, ajaxOptions: new AjaxOptions
                {
                    InsertionMode = insertionMode,
                    UpdateTargetId = "LogContent",
                    Confirm = $"Deletion of log {log.Id} is permanent. Continue?",
                    OnFailure = fail,
                    LoadingElementId = ajax
                }))
                {
                    @Html.AntiForgeryToken()
                   <button class="link-button text-danger" type="submit"><span class="glyphicon glyphicon-trash"></span></button>
                }
            </td>
        }

However with the server side processing I'm not sure how to add the buttons that utilize this Ajax.BeginForm. The reason for that is the Edit has a modal pop up and when it's closed the table that the button is on will update without refreshing the entire page or redirecting.

So my question:
How can I add a custom button to my Ajax data that has the Ajax.BeginForm that will allow a modal to pop up and refresh the page once the modal closes?