Math.E Field
[ This article is for Windows Phone 8 developers. If you’re developing for Windows 10, see the latest documentation. ]
Represents the natural logarithmic base, specified by the constant, e.
Assembly: mscorlib (in mscorlib.dll)
The following example compares E with the value calculated from a power series.
// Example for the Math.E field. using System; class Example { public static void Demo(System.Windows.Controls.TextBlock outputBlock) { outputBlock.Text += String.Format("This example of Math.E == {0:E16}\n" + "generates the following output.\n", Math.E); outputBlock.Text += "Define the power series PS(n) = Sum(k->0,n)[1/k!]" + "\n"; outputBlock.Text += " (limit n->infinity)PS(n) == e" + "\n"; outputBlock.Text += "Display PS(n) and Math.E - PS(n), " + "and stop when delta < 1.0E-15\n" + "\n"; CalcPowerSeries(outputBlock); } // Approximate E with a power series. static void CalcPowerSeries(System.Windows.Controls.TextBlock outputBlock) { double factorial = 1.0; double PS = 0.0; // Stop iterating when the series converges, // and prevent a runaway process. for (int n = 0; n < 999 && Math.Abs(Math.E - PS) > 1.0E-15; n++) { // Calculate a running factorial. if (n > 0) factorial *= (double)n; // Calculate and display the power series. PS += 1.0 / factorial; outputBlock.Text += String.Format("PS({0:D2}) == {1:E16}, Math.E - PS({0:D2}) == {2:E16}\n", n, PS, Math.E - PS); } } } /* This example of Math.E == 2.7182818284590451E+000 generates the following output. Define the power series PS(n) = Sum(k->0,n)[1/k!] (limit n->infinity)PS(n) == e Display PS(n) and Math.E - PS(n), and stop when delta < 1.0E-15 PS(00) == 1.0000000000000000E+000, Math.E - PS(00) == 1.7182818284590451E+000 PS(01) == 2.0000000000000000E+000, Math.E - PS(01) == 7.1828182845904509E-001 PS(02) == 2.5000000000000000E+000, Math.E - PS(02) == 2.1828182845904509E-001 PS(03) == 2.6666666666666665E+000, Math.E - PS(03) == 5.1615161792378572E-002 PS(04) == 2.7083333333333330E+000, Math.E - PS(04) == 9.9484951257120535E-003 PS(05) == 2.7166666666666663E+000, Math.E - PS(05) == 1.6151617923787498E-003 PS(06) == 2.7180555555555554E+000, Math.E - PS(06) == 2.2627290348964380E-004 PS(07) == 2.7182539682539684E+000, Math.E - PS(07) == 2.7860205076724043E-005 PS(08) == 2.7182787698412700E+000, Math.E - PS(08) == 3.0586177750535626E-006 PS(09) == 2.7182815255731922E+000, Math.E - PS(09) == 3.0288585284310443E-007 PS(10) == 2.7182818011463845E+000, Math.E - PS(10) == 2.7312660577649694E-008 PS(11) == 2.7182818261984929E+000, Math.E - PS(11) == 2.2605521898810821E-009 PS(12) == 2.7182818282861687E+000, Math.E - PS(12) == 1.7287637987806193E-010 PS(13) == 2.7182818284467594E+000, Math.E - PS(13) == 1.2285727990501982E-011 PS(14) == 2.7182818284582302E+000, Math.E - PS(14) == 8.1490370007486490E-013 PS(15) == 2.7182818284589949E+000, Math.E - PS(15) == 5.0182080713057076E-014 PS(16) == 2.7182818284590429E+000, Math.E - PS(16) == 2.2204460492503131E-015 PS(17) == 2.7182818284590455E+000, Math.E - PS(17) == -4.4408920985006262E-016 */
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