{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "In this notebook, we review some properties of the complex exponential function. This function plays an important role for defining and understanding the Fourier transform, see Section 2.3.2 of [Müller, FMP, Springer 2015].\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Power Series\n", "\n", "One encounters the **real exponential function** $\\exp:\\mathbb{R}\\to \\mathbb{R}$ in the context of many mathematical applications, and the function can be characterized in many different ways. Historically, the exponential function was studied already by **Johann Bernoulli** in the $17^\\mathrm{th}$ century when considering **interest rates**: Assume that an amount of $1$ earns an interest $a$ at an annual rate compounded monthly. Then the interest earned each month is $\\frac{a}{12}$ times the current value, so that each month the total value is multiplied by $\\left(1+\\frac{a}{12}\\right)$ and the value at the end of the year is $\\left(1+\\frac{a}{12}\\right)^{12}$. In case the interest is compounded every day, it becomes $\\left(1+\\frac{a}{365}\\right)^{365}$. Letting the time intervals grow per year by making them shorter leads to the limit definition of the exponential function\n", "\n", "$$\\exp(a) = \\mathrm{lim}_{n\\to\\infty} \\left(1+\\frac{a}{n}\\right)^{n},$$\n", "\n", "which was first given by **Leonhard Euler**. The constant $e:=\\exp(1)\\approx 2.71828 \\ldots$ is also known as **Euler's number**. By expanding the $n$-fold product in the above definition, one can show that the exponential function can also be expressed by the following power series:\n", "\n", "$$\\exp(a) := \\sum_{n=0}^{\\infty} \\frac{a^n}{n!} = 1 + a + \\frac{a^2}{1 \\cdot 2} + \\frac{a^3}{1 \\cdot 2 \\cdot 3} + \\dots$$\n", "\n", "with $a\\in\\mathbb{R}$. Replacing in the power series the real-valued variable $a\\in\\mathbb{R}$ by a complex-valued variable $c\\in\\mathbb{C}$, one still obtains the **complex exponential function** $\\exp:\\mathbb{C}\\to \\mathbb{C}$ given by \n", "\n", "$$\\exp(c) := \\sum_{n=0}^{\\infty} \\frac{c^n}{n!} = 1 + c + \\frac{c^2}{1 \\cdot 2} + \\frac{c^3}{1 \\cdot 2 \\cdot 3} + \\dots$$\n", "\n", "Based on the definition of the complex exponential function, one can also extend the definition of trigonometric functions (e.g. $\\sin$ and $\\cos$) to complex arguments.\n", "\n", "The following implementation yields an approximation of the power series by considering only the first $N$ terms specified by the parameter $N\\in\\mathbb{N}$. For the case $c=1$, this yields an approximation for the number $e$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T09:00:02.939773Z", "iopub.status.busy": "2024-02-15T09:00:02.939466Z", "iopub.status.idle": "2024-02-15T09:00:04.032768Z", "shell.execute_reply": "2024-02-15T09:00:04.032105Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Approximation (N = 1): 1\n", "Approximation (N = 2): 2.0\n", "Approximation (N = 4): 2.6666666666666665\n", "Approximation (N = 8): 2.7182539682539684\n", "Approximation (N = 12): 2.718281826198493\n", "Numpy: 2.718281828459045\n" ] } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "%matplotlib inline\n", "\n", "def exp_power_series(c, N):\n", " \"\"\"Compute power series for exponential function\n", "\n", " Notebook: C2_ExponentialFunction.ipynb\n", "\n", " Args:\n", " c: Complex number\n", " N: Number of summands used for approximation\n", "\n", " Returns:\n", " exp_c: Approximation of exp(c)\n", " \"\"\" \n", " exp_c = 1\n", " c_power = 1\n", " nfac = 1\n", " for n in range(1, N):\n", " nfac *= n\n", " c_power *= c \n", " exp_c += c_power / nfac\n", " return exp_c\n", "\n", "c=1\n", "print('Approximation (N = 1):', exp_power_series(c, 1))\n", "print('Approximation (N = 2):', exp_power_series(c, 2))\n", "print('Approximation (N = 4):', exp_power_series(c, 4))\n", "print('Approximation (N = 8):', exp_power_series(c, 8))\n", "print('Approximation (N = 12):', exp_power_series(c, 12))\n", "print('Numpy: ', np.exp(c))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exponentiation Identity and Euler's Formula \n", "\n", "Based on the power series definition, one may prove two famous formulas of the exponential function that explain many of its properties. The first formula is knowns as **exponentiation identity** and says that \n", "\n", "$$\n", " \\exp(c_1 + c_2) = \\exp(c_1)\\cdot \\exp(c_2)\n", "$$\n", "\n", "for any complex numbers $c_1, c_2\\in\\mathbb{C}$. In particular, this property explains the exponential increase for real arguments. For example, \n", "\n", "$$\n", " \\exp(n) = \\exp(1+1+\\ldots +1) = \\exp(1)^n = e^n\n", "$$\n", "\n", "for $n\\in\\mathbb{N}$. The second famous formula, which is known as **Euler's formula**, relates the values of the exponential function at purely imaginary arguments to trigonometric functions. It states that for the complex number $c = i\\gamma$ with some real-valued $\\gamma\\in\\mathbb{R}$ one has the identity \n", "\n", "$$\\mathrm{exp}(i\\gamma) = \\cos(\\gamma) + i\\sin(\\gamma) .$$\n", "\n", "Actually, starting with the real sine and cosine functions, one often defines $\\mathrm{exp}(i\\gamma)$ by means of the Euler formula (rather than using the power series). This explains the periodic behavior of the real and imaginary part of $\\exp$ along the imaginary (vertical) axis as shown in the next figure. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T09:00:04.064130Z", "iopub.status.busy": "2024-02-15T09:00:04.063860Z", "iopub.status.idle": "2024-02-15T09:00:04.496137Z", "shell.execute_reply": "2024-02-15T09:00:04.495628Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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