Math.E-Feld

Stellt die Basis des natürlichen Logarithmus durch die Konstante e dar.

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

Syntax

'Declaration
Public Const E As Double
'Usage
Dim value As Double

value = Math.E

public const double E

public:
literal double E

public static final double E

public const var E : double

Hinweise

Der Wert dieses Felds ist 2,7182818284590452354.

Beispiel

Im folgenden Beispiel wird E mit dem Wert verglichen, der in einer Potenzreihe berechnet wurde.

' 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

// 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.
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( "PS({0:D2}) == {1:E16},  Math::E - PS({0:D2}) == {2:E16}", n, PS, Math::E - PS );

   }
}

int 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();
}

/*
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
*/

Plattformen

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

.NET Framework unterstützt nicht alle Versionen sämtlicher Plattformen. Eine Liste der unterstützten Versionen finden Sie unter Systemanforderungen.

Versionsinformationen

.NET Framework

Unterstützt in: 2.0, 1.1, 1.0

.NET Compact Framework

Unterstützt in: 2.0, 1.0

Siehe auch

Referenz

Math-Klasse
Math-Member
System-Namespace