tgamma() method in C/C++ with Examples

The tgamma() function is defined in header math.h header in C and cmath library in C++. This function is used to compute the gamma function of an argument passed to the function.

Syntax of tgamma()

float tgamma(float x);
double tgamma(double x);
long double tgamma(long double x);

Parameters

x: The value whose gamma function is to be computed. It can be float, double or long double.

Return Value

• This function returns the gamma function value of x. 
• For x = 0: +inf/-inf
• For x = -inf: NAN
• For x = +inf: +inf
• For x = -ve: NAN
• For x = NAN: NAN

Errors in tgamma() Function

There are two types of errors that usually occur with tgamma() method:

1. Range errors
   • Overflow range error: This occurs when the magnitude of the parameter x is very large.
   • Underflow range error: This occurs when the magnitude of the parameter x is very small.
     
2. Domain/Pole errors
   If x is zero or a negative integer for which the function is asymptotic, it may cause a domain error or a pole error (or none, depending on implementation).

Example of tgamma Function

Below example demonstrate the use of tgamma() function in C/C++:

C

// C program to show the use of tgamma() method
#include <math.h>
#include <stdio.h>

int main()
{

    // Example 1
    float x = 0.0;
    printf("For x = %f, tgamma(x) = %f\n", x, tgamma(x));

    // Example 2
    x = -18.0 / 0.0;
    printf("For x = %f, tgamma(x) = %f\n", x, tgamma(x));

    // Example 3
    x = 10.0 / 0.0;
    printf("For x = %f, tgamma(x) = %f\n", x, tgamma(x));

    // Example 4
    x = 0.0 / 0.0;
    printf("For x = %f, tgamma(x) = %f", x, tgamma(x));

    return 0;
}

C++

// C++ program to show the use of tgamma() method
#include <cmath>
#include <iostream>

using namespace std;

// Driver code
int main()
{

    // Example 1
    float x = 0.0;
    cout << "For x = " << x << ", tgamma(x) = " << tgamma(x)
         << endl;

    // Example 2
    x = -18.0 / 0.0;
    cout << "For x = " << x << ", tgamma(x) = " << tgamma(x)
         << endl;

    // Example 3
    x = 10.0 / 0.0;
    cout << "For x = " << x << ", tgamma(x) = " << tgamma(x)
         << endl;

    // Example 4
    x = 0.0 / 0.0;
    cout << "For x = " << x
         << ", tgamma(x) = " << tgamma(x);

    return 0;
}

Output

For x = 0.000000, tgamma(x) = inf
For x = -inf, tgamma(x) = nan
For x = inf, tgamma(x) = inf
For x = -nan, tgamma(x) = -nan