Package org.drip.specialfunction.loggamma

Class InfiniteSumEstimator

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.numerical.estimation.R1ToR1Estimator
org.drip.specialfunction.loggamma.InfiniteSumEstimator
public abstract class InfiniteSumEstimator
extends R1ToR1Estimator
InfiniteSumEstimator estimates Log Gamma using the Infinite Series Infinite Sum. The References are:

  • Blagouchine, I. V. (2014): Re-discovery of Malmsten's Integrals, their Evaluation by Contour Integration Methods, and some Related Results Ramanujan Journal 35 (1) 21-110
  • Borwein, J. M., and R. M. Corless (2017): Gamma Function and the Factorial in the Monthly https://arxiv.org/abs/1703.05349 arXiv
  • Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function American Mathematical Monthly 66 (10) 849-869
  • Whitaker, E. T., and G. N. Watson (1996): A Course on Modern Analysis Cambridge University Press New York
  • Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
It provides the following functionality:
  • Compute the Euler Infinite Sum Series of Log Gamma Estimator
  • Compute the Weierstrass Infinite Sum Series of Log Gamma Estimator
  • Compute the Fourier Infinite Sum Series of Log Gamma Estimator
  • Compute the Blagouchine (2015) Infinite Sum Series of Log Gamma Estimator
  • InfiniteSumEstimator Constructor

Module Computational Core Module
Library Function Analysis Library
Project Special Function Implementation and Analysis
Package Analytic/Series/Integral Log Gamma Estimators
Author:
Lakshmi Krishnamurthy

  • Method Details

    • Euler

      public static final InfiniteSumEstimator Euler​(int termCount)
      Compute the Euler Infinite Sum Series of Log Gamma Estimator
      Parameters:
      termCount - Number of Terms in the Estimation
      Returns:
      The Euler Infinite Sum Series of Log Gamma Estimator

    • Weierstrass

      public static final InfiniteSumEstimator Weierstrass​(int termCount)
      Compute the Weierstrass Infinite Sum Series of Log Gamma Estimator
      Parameters:
      termCount - Number of Terms in the Estimation
      Returns:
      The Weierstrass Infinite Sum Series of Log Gamma Estimator

    • Fourier

      public static final InfiniteSumEstimator Fourier​(int termCount)
      Compute the Fourier Infinite Sum Series of Log Gamma Estimator
      Parameters:
      termCount - Number of Terms in the Estimation
      Returns:
      The Fourier Infinite Sum Series of Log Gamma Estimator

    • Blagouchine2015

      public static final InfiniteSumEstimator Blagouchine2015​(int termCount)
      Compute the Blagouchine (2015) Infinite Sum Series of Log Gamma Estimator
      Parameters:
      termCount - Number of Terms in the Estimation
      Returns:
      The Blagouchine (2015) Infinite Sum Series of Log Gamma Estimator

    • infiniteSumSeries

      public R1ToR1Series infiniteSumSeries()
      Retrieve the Underlying Infinite Sum Series
      Returns:
      The Underlying Infinite Sum Series

    • seriesEstimateNative

      public R1Estimate seriesEstimateNative​(double x)
      Description copied from class: R1ToR1Estimator
      Compute the Built-in Higher Order Series Estimates
      Overrides:
      seriesEstimateNative in class R1ToR1Estimator
      Parameters:
      x - X
      Returns:
      The Built-in Higher Order Series Estimates

    • poleResidue

      public PoleResidue poleResidue​(double x)
      Description copied from class: R1ToR1
      Compute the Residue if the Variate is a Pole
      Overrides:
      poleResidue in class R1ToR1
      Parameters:
      x - Variate
      Returns:
      The Residue if the Variate is a Pole