/**

* @function exponentialFunction

* @description Calculates the n+1 th order Taylor series approximation of exponential function e^x given n

* @param {Integer} power

* @param {Integer} order - 1

* @returns exponentialFunction(2,20) = 7.3890560989301735

* @url https://en.wikipedia.org/wiki/Exponential_function

*/

function exponentialFunction(power, n) {

let output = 0

let fac = 1

if (isNaN(power) || isNaN(n) || n < 0) {

throw new TypeError('Invalid Input')

}

if (n === 0) {

return 1

}

for (let i = 0; i < n; i++) {

output += power ** i / fac

fac *= i + 1

}

return output

}

export { exponentialFunction }