JSFiddle - React, Tailwind, and code Playground

JavaScript

function carousel(array, index, n) {
    var result = [];

    for (var i = index - n, len = array.length; i <= index + n; i++) {
        result.push(array[i < 0 ? len + i : i > len - 1 ? i - len : i]);
    }

    return result;
}

var array = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
    index = 8,
    n = 3;

console.log(carousel(array, index, n));