mathnet-numerics/examples/examples-csharp/SpecialFunctions/Gamma.cs

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using System;
using MathNet.Numerics;

namespace Examples.SpecialFunctionsExamples
{
    /// <summary>
    /// Special Functions: Gamma
    /// </summary>
    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/Gamma.html"/>
    public class Gamma : IExample
    {
        /// <summary>
        /// Gets the name of this example
        /// </summary>
        public string Name
        {
            get
            {
                return "Special Functions: Gamma";
            }
        }

        /// <summary>
        /// Gets the description of this example
        /// </summary>
        public string Description
        {
            get
            {
                return "Gamma, incomplete Gamma, regularized Gamma";
            }
        }

        /// <summary>
        /// Run example
        /// </summary>
        /// <seealso cref="http://en.wikipedia.org/wiki/Gamma_function">Gamma function</seealso>
        public void Run()
        {
            // 1. Compute the Gamma function of 10
            Console.WriteLine(@"1. Compute the Gamma function of 10");
            Console.WriteLine(SpecialFunctions.Gamma(10).ToString("N"));
            Console.WriteLine();

            // 2. Compute the logarithm of the Gamma function of 10
            Console.WriteLine(@"2. Compute the logarithm of the Gamma function of 10");
            Console.WriteLine(SpecialFunctions.GammaLn(10).ToString("N"));
            Console.WriteLine();

            // 3. Compute the lower incomplete gamma(a, x) function at a = 10, x = 14 
            Console.WriteLine(@"3. Compute the lower incomplete gamma(a, x) function at a = 10, x = 14");
            Console.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 14).ToString("N"));
            Console.WriteLine();

            // 4. Compute the lower incomplete gamma(a, x) function at a = 10, x = 100 
            Console.WriteLine(@"4. Compute the lower incomplete gamma(a, x) function at a = 10, x = 100");
            Console.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 100).ToString("N"));
            Console.WriteLine();

            // 5. Compute the upper incomplete gamma(a, x) function at a = 10, x = 0 
            Console.WriteLine(@"5. Compute the upper incomplete gamma(a, x) function at a = 10, x = 0");
            Console.WriteLine(SpecialFunctions.GammaUpperIncomplete(10, 0).ToString("N"));
            Console.WriteLine();

            // 6. Compute the upper incomplete gamma(a, x) function at a = 10, x = 10 
            Console.WriteLine(@"6. Compute the upper incomplete gamma(a, x) function at a = 10, x = 100");
            Console.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 10).ToString("N"));
            Console.WriteLine();

            // 7. Compute the lower regularized gamma(a, x) function at a = 10, x = 14 
            Console.WriteLine(@"7. Compute the lower regularized gamma(a, x) function at a = 10, x = 14");
            Console.WriteLine(SpecialFunctions.GammaLowerRegularized(10, 14).ToString("N"));
            Console.WriteLine();

            // 8. Compute the lower regularized gamma(a, x) function at a = 10, x = 100 
            Console.WriteLine(@"8. Compute the lower regularized gamma(a, x) function at a = 10, x = 100");
            Console.WriteLine(SpecialFunctions.GammaLowerRegularized(10, 100).ToString("N"));
            Console.WriteLine();

            // 9. Compute the upper regularized gamma(a, x) function at a = 10, x = 0 
            Console.WriteLine(@"9. Compute the upper regularized gamma(a, x) function at a = 10, x = 0");
            Console.WriteLine(SpecialFunctions.GammaUpperRegularized(10, 0).ToString("N"));
            Console.WriteLine();

            // 10. Compute the upper regularized gamma(a, x) function at a = 10, x = 10 
            Console.WriteLine(@"10. Compute the upper regularized gamma(a, x) function at a = 10, x = 100");
            Console.WriteLine(SpecialFunctions.GammaUpperRegularized(10, 10).ToString("N"));
            Console.WriteLine();
        }
    }
}