CSHARP

maclaurin series

/// <summary>
///     Maclaurin series calculates nonlinear functions approximation
///     starting from point x = 0 in a form of infinite power series:
///     f(x) = f(0) + f'(0) * x + ... + (f'n(0) * (x ^ n)) / n! + ...,
///     where n is natural number.
/// </summary>
public static class Maclaurin
{
  /// <summary>
  ///     Calculates approximation of e^x function:
  ///     e^x = 1 + x + x^2 / 2! + ... + x^n / n! + ...,
  ///     where n is number of terms (natural number),
  ///     and x is given point (rational number).
  /// </summary>
  /// <param name="x">Given point.</param>
  /// <param name="n">The number of terms in polynomial.</param>
  /// <returns>Approximated value of the function in the given point.</returns>
  public static double Exp(double x, int n) =>
    Enumerable.Range(0, n).Sum(i => ExpTerm(x, i));

  public static double Sin(double x, int n) =>
    Enumerable.Range(0, n).Sum(i => SinTerm(x, i));

  public static double Cos(double x, int n) =>
    Enumerable.Range(0, n).Sum(i => CosTerm(x, i));

  public static double Exp(double x, double error = 0.00001) => ErrorTermWrapper(x, error, ExpTerm);

  public static double Sin(double x, double error = 0.00001) => ErrorTermWrapper(x, error, SinTerm);

  public static double Cos(double x, double error = 0.00001) => ErrorTermWrapper(x, error, CosTerm);

  private static double ErrorTermWrapper(double x, double error, Func<double, int, double> term)
  {
    if (error <= 0.0 || error >= 1.0)
    {
      throw new ArgumentException("Error value is not on interval (0.0; 1.0).");
    }

    var i = 0;
    var termCoefficient = 0.0;
    var result = 0.0;

    do
    {
      result += termCoefficient;
      termCoefficient = term(x, i);
      i++;
    }
    while (Math.Abs(termCoefficient) > error);

    return result;
  }

  private static double ExpTerm(double x, int i) => Math.Pow(x, i) / Factorial.Calculate(i);

  private static double SinTerm(double x, int i) =>
    Math.Pow(-1, i) / Factorial.Calculate(2 * i + 1) * Math.Pow(x, 2 * i + 1);

  private static double CosTerm(double x, int i) =>
    Math.Pow(-1, i) / Factorial.Calculate(2 * i) * Math.Pow(x, 2 * i);
}