Math.E Pole
Definice
Důležité
Některé informace platí pro předběžně vydaný produkt, který se může zásadně změnit, než ho výrobce nebo autor vydá. Microsoft neposkytuje žádné záruky, výslovné ani předpokládané, týkající se zde uváděných informací.
Představuje přirozený logaritmický základ určený konstantou e
.
public: double E = 2.7182818284590451;
public const double E = 2.7182818284590451;
val mutable E : double
Public Const E As Double = 2.7182818284590451
Hodnota pole
Value = 2.7182818284590451Příklady
Následující příklad porovnává E s hodnotou vypočítanou z mocninné řady.
// 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
Poznámky
Hodnota tohoto pole je 2,7182818284590451.
Platí pro
Spolupracujte s námi na GitHubu
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