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std::tgamma

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definiert in Header <cmath>
float       tgamma( float arg );
(seit C++11)
double      tgamma( double arg );
(seit C++11)
long double tgamma( long double arg );
(seit C++11)
double      tgamma( Integral arg );
(seit C++11)
Berechnet den Gamma-Funktion der arg .
Original:
Computes the Gamma-Funktion of arg.
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Inhaltsverzeichnis

[Bearbeiten] Parameter

arg -
Floating-Point-Wert
Original:
floating point value
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[Bearbeiten] Rückgabewert

Der Wert der Gammafunktion arg, das heißt
0
targ-1
e-t dt
.
Original:
The value of the gamma function of arg, that is
0
targ-1
e-t dt
.
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Wenn arg eine natürliche Zahl ist, ist std::tgamma(arg) die Fakultät arg-1 .
Original:
If arg is a natural number, std::tgamma(arg) is the factorial of arg-1.
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[Bearbeiten] Ausnahmen

Wenn arg negativ ist, kann Domain-Fehler auftreten, und FE_INVALID angehoben werden kann .
Original:
If arg is negative, domain error may occur and FE_INVALID may be raised.
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Wenn arg Null ist, kann pole Fehler auftreten und FE_DIVBYZERO angehoben werden kann .
Original:
If arg is zero, pole error may occur and FE_DIVBYZERO may be raised.
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Wenn arg zu groß ist, können die Reichweite Fehler auftreten und FE_OVERFLOW angehoben werden kann .
Original:
If arg is too large, range error may occur and FE_OVERFLOW may be raised.
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Wenn arg zu klein ist, können die Reichweite Fehler auftreten und FE_UNDERFLOW angehoben werden kann .
Original:
If arg is too small, range error may occur and FE_UNDERFLOW may be raised.
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[Bearbeiten] Notes

Viele Implementierungen berechnet die genaue Integer-Domain-faktoriellen, wenn das Argument eine hinreichend kleine Zahl .
Original:
Many implementations calculate the exact integer-domain factorial if the argument is a sufficiently small integer.
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[Bearbeiten] Beispiel

#include <iostream>
#include <cmath>
double factorial(double arg)
{
    return std::tgamma(arg + 1);
}
int main()
{
    std::cout << "The factorial of 5 is " << factorial(5) << '\n'
              << "The factorial of 100 is " << factorial(100) << '\n';
}

Output:

The factorial of 5 is 120
The factorial of 100 is 9.33262e+157


[Bearbeiten] Siehe auch

(C++11)
natürlichen Logarithmus der Gamma-Funktion
Original:
natural logarithm of the gamma function
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(Funktion) [edit]

[Bearbeiten] Externer Links

Weisstein, Eric W. "Gamma Function." Von MathWorld - A Wolfram Web Resource .
Original:
Weisstein, Eric W. "Gamma Function." From MathWorld--A Wolfram Web Resource.
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