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# Trigamma

Evaluates the Trigamma function.
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C++
Excel

## Trigamma

 doubletrigamma( double x )
This component evaluates the Trigamma function with given parameters, defined by the second derivative of the logarithm of the Gamma function:

$\psi_1(x)&space;=&space;\frac{\mathrm{d}^2}{\mathrm{d}x^2}&space;\mathrm{ln}&space;\Gamma(x)$

In the following example, arguments from the [3, 4] interval are used, with step equal to 0.2, to evaluate the Trigamma function.

### Example 1

#include <codecogs/maths/special/gamma/trigamma.h>
#include <iostream>
#include <iomanip>

int main()
{
std::cout << std::setprecision(10);
for (double x = 3; x < 5; x += 0.2)
{
std::cout << "Trigamma(" << x << ") = ";
std::cout << Maths::Special::Gamma::trigamma(x) << std::endl;
}
return 0;
}

### Output

Trigamma(3) = 0.3949340655
Trigamma(3.2) = 0.3663211898
Trigamma(3.4) = 0.3415413972
Trigamma(3.6) = 0.3198778986
Trigamma(3.8) = 0.3007811415
Trigamma(4) = 0.2838229544
Trigamma(4.2) = 0.2686649398
Trigamma(4.4) = 0.2550362069
Trigamma(4.6) = 0.2427174048
Trigamma(4.8) = 0.2315290639

### References

John Burkardt's library of statistical C++ routines, http://www.csit.fsu.edu/~burkardt/cpp_src/prob/prob.html

### Parameters

 x the argument of the trigamma function

### Returns

An approximation of the Trigamma function with the given argument.

### Authors

Lucian Bentea (September 2005)
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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