Add an algorithm to find Taylor series approximation of exponential function

prashalruchiranga · prashalruchiranga · commit f8dc85c31188 · 2022-10-10T12:48:30.000+05:30
diff --git a/Maths/ExponentialFunction.js b/Maths/ExponentialFunction.js
@@ -0,0 +1,21 @@
+let powerOfX = 1
+let factorial = 1
+/**
+ * @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(18,4) = 18.4
+ * @url https://en.wikipedia.org/wiki/Exponential_function
+ */
+function exponentialFunction (power, n) {
+  if (n === 0) { return 1 }
+  const recursion = exponentialFunction(power, n - 1)
+  powerOfX = powerOfX * power
+  factorial = factorial * n
+  return recursion + powerOfX / factorial
+}
+
+export {
+  exponentialFunction
+}
diff --git a/Maths/test/ExponentialFunction.test.js b/Maths/test/ExponentialFunction.test.js
@@ -0,0 +1,8 @@
+import { exponentialFunction } from '../ExponentialFunction'
+
+describe('exponentialFunction', () => {
+  it('with a power of 5 and order of 21', () => {
+    const ex = exponentialFunction(5, 20)
+    expect(ex).toBe(148.4131470673818)
+  })
+})
