Math.E Feld

Referenz

Definition

Namespace:: System

Assembly:: System.Runtime.Extensions.dll

Assembly:: System.Runtime.dll

Assembly:: mscorlib.dll

Assembly:: netstandard.dll

Quelle:: Math.cs

Quelle:: Math.cs

Quelle:: Math.cs

Wichtig

Einige Informationen beziehen sich auf Vorabversionen, die vor dem Release ggf. grundlegend überarbeitet werden. Microsoft übernimmt hinsichtlich der hier bereitgestellten Informationen keine Gewährleistungen, seien sie ausdrücklich oder konkludent.

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

public: double E = 2.7182818284590451;

public const double E = 2.7182818284590451;

val mutable E : double

Public Const E As Double  = 2.7182818284590451

Feldwert

Value = 2.7182818284590451

Double

Beispiele

Im folgenden Beispiel wird E mit dem Wert verglichen, der aus einer Leistungsreihe berechnet wird.

// 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.
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.
open System

// Approximate E with a power series.
let calcPowerSeries () =
    let mutable factorial = 1.
    let mutable PS = 0.
    let mutable n = 0
    // Stop iterating when the series converges,
    // and prevent a runaway process.
    while n < 999 && abs (Math.E - PS) > 1.0E-15 do
        // Calculate a running factorial.
        if n > 0 then
            factorial <- factorial * double n

        // Calculate and display the power series.
        PS <- PS + 1. / factorial
        printfn $"PS({n:D2}) = {PS:E16},  Math.E - PS({n:D2}) = {Math.E - PS:E16}"
        n <- n + 1

printfn $"This example of Math.E = {Math.E:E16}\ngenerates the following output.\n"    
printfn "Define the power series PS(n) = Sum(k->0,n)[1/k!]"
printfn " (limit n->infinity)PS(n) = e"
printfn "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.
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
       
    ' 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
    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

Hinweise

Der Wert dieses Felds ist 2,7182818284590451.

Gilt für:

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