// <copyright file="Harmonic.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2011 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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// <contribution>
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// Cephes Math Library, Stephen L. Moshier
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// ALGLIB 2.0.1, Sergey Bochkanov
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// </contribution>
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using System;
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// ReSharper disable CheckNamespace
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namespace IStation.Numerics
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// ReSharper restore CheckNamespace
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{
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/// <summary>
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/// This partial implementation of the SpecialFunctions class contains all methods related to the harmonic function.
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/// </summary>
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public static partial class SpecialFunctions
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{
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/// <summary>
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/// Computes the <paramref name="t"/>'th Harmonic number.
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/// </summary>
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/// <param name="t">The Harmonic number which needs to be computed.</param>
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/// <returns>The t'th Harmonic number.</returns>
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public static double Harmonic(int t)
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{
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return Constants.EulerMascheroni + DiGamma(t + 1.0);
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}
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/// <summary>
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/// Compute the generalized harmonic number of order n of m. (1 + 1/2^m + 1/3^m + ... + 1/n^m)
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/// </summary>
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/// <param name="n">The order parameter.</param>
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/// <param name="m">The power parameter.</param>
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/// <returns>General Harmonic number.</returns>
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public static double GeneralHarmonic(int n, double m)
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{
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double sum = 0;
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for (int i = 0; i < n; i++)
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{
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sum += Math.Pow(i + 1, -m);
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}
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return sum;
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}
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}
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}
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