# Math.E Field

.NET Framework 2.0

Represents the natural logarithmic base, specified by the constant, e.

Namespace: System
Assembly: mscorlib (in mscorlib.dll)

## Syntax

```public const double E
```
```public static final double E
```
```public const var E : double
```

## Remarks

The value of this field is 2.7182818284590452354.

## Example

The following example compares E with the value calculated from a power series.

```// Example for the Math.E field.
using System;

class EField
{
public static void Main()
{
Console.WriteLine(
"This example of Math.E == {0:E16}\n" +
"generates the following output.\n",
Math.E );
Console.WriteLine(
"Define the power series PS(n) = Sum(k->0,n)[1/k!]" );
Console.WriteLine( " (limit n->infinity)PS(n) == e" );
Console.WriteLine(
"Display PS(n) and Math.E - PS(n), " +
"and stop when delta < 1.0E-15\n" );

CalcPowerSeries();
}

// Approximate E with a power series.
static void CalcPowerSeries()
{
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;
Console.WriteLine(
"PS({0:D2}) == {1:E16},  Math.E - PS({0:D2}) == {2:E16}",
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
*/

```
```// Example for the Math.E field.
import System.*;

class EField
{
public static void main(String[] args)
{
Console.WriteLine("This example of Math.E == {0}\n"
+ "generates the following output.\n",
((System.Double)Math.E).ToString("E16"));
Console.WriteLine("Define the power series PS(n) = Sum(k->0,n)[1/k!]");
Console.WriteLine(" (limit n->infinity)PS(n) == e");
Console.WriteLine(("Display PS(n) and Math.E - PS(n), "
+ "and stop when delta < 1.0E-15\n"));
CalcPowerSeries();
} //main

// Approximate E with a power series.
static void CalcPowerSeries()
{
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 && System.Math.Abs((Math.E - pS)) > 1E-15; n++) {
// Calculate a running factorial.
if (n > 0) {
factorial *= (double)(n);
}

// Calculate and display the power series.
pS += 1.0 /factorial;
Console.WriteLine("PS({0}) == {1},  Math.E - PS({0}) == {2}",
((System.Int32) n).ToString("D2"),
((System.Double )pS).ToString("E16"),
((System.Double )(Math.E - pS)).ToString("E16"));
}
} //CalcPowerSeries
} //EField

/*
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
*/

```

## Platforms

Windows 98, Windows 2000 SP4, Windows CE, Windows Millennium Edition, Windows Mobile for Pocket PC, Windows Mobile for Smartphone, Windows Server 2003, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP SP2, Windows XP Starter Edition

The .NET Framework does not support all versions of every platform. For a list of the supported versions, see System Requirements.

## Version Information

#### .NET Framework

Supported in: 2.0, 1.1, 1.0

#### .NET Compact Framework

Supported in: 2.0, 1.0