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E Field

# Math.E Field

.NET Framework 4.6 and 4.5

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

Namespace:  System
Assemblies:   mscorlib (in mscorlib.dll)
System.Runtime.Extensions (in System.Runtime.Extensions.dll)

## Syntax

```public const double E
```

## Remarks

The value of this field is 2.7182818284590452354.

## Examples

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
*/
```

## Version Information

#### .NET Framework

Supported in: 4.6, 4.5, 4, 3.5, 3.0, 2.0, 1.1

#### .NET Framework Client Profile

Supported in: 4, 3.5 SP1

#### XNA Framework

Supported in: 3.0, 2.0, 1.0

#### .NET for Windows Phone apps

Supported in: Windows Phone 8.1, Windows Phone Silverlight 8.1, Windows Phone Silverlight 8

#### Portable Class Library

Supported in: Portable Class Library