E Field
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Math.E Field

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

[Visual Basic]
Public Const E As Double
[C#]
public const double E;
[C++]
public: const double E;
[JScript]
public var E : double;

Remarks

The value of this field is 2.7182818284590452354.

Example

[Visual Basic, C#, C++] The following example compares E with the value calculated from a power series.

[Visual Basic] 
' Example for the Math.E field.
Imports System
Imports Microsoft.VisualBasic

Module EField
       
    Sub Main()
        Console.WriteLine( _
            "This example of Math.E = {0:E16}" & vbCrLf & _
            "generates the following output." & vbCrLf, _
            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" & vbCrLf )
          
        CalcPowerSeries()
    End Sub 'Main
       
    ' Approximate E with a power series.
    Sub CalcPowerSeries()
        Dim factorial As Double = 1.0
        Dim PS As Double = 0.0
          
        ' Stop iterating when the series converges,
        ' and prevent a runaway process.
        Dim n As Integer
        For n = 0 To 999

            ' Calculate a running factorial.
            If n > 0 Then
                factorial *= System.Convert.ToDouble(n)
            End If 

            ' 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 )

            ' Exit when the series converges.
            If Math.Abs( Math.E - PS ) < 1.0E-15 Then
                Exit For
            End If
        Next n
    End Sub 'CalcPowerSeries
    End Module '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

[C#] 
// 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
*/

[C++] 
// Example for the Math::E field.
#using <mscorlib.dll>
using namespace System;

// Approximate E with a power series.
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( 
            S"PS({0:D2}) == {1:E16},  Math::E - PS({0:D2}) == {2:E16}",
            __box(n), __box(PS), __box(Math::E - PS) );
    }
}

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

    CalcPowerSeries();
}

/*
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
*/

[JScript] No example is available for JScript. To view a Visual Basic, C#, or C++ example, click the Language Filter button Language Filter in the upper-left corner of the page.

Requirements

Platforms: Windows 98, Windows NT 4.0, Windows Millennium Edition, Windows 2000, Windows XP Home Edition, Windows XP Professional, Windows Server 2003 family, .NET Compact Framework, Common Language Infrastructure (CLI) Standard

See Also

Math Class | Math Members | System Namespace

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