Package org.drip.specialfunction.gamma

Class StirlingSeries

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.numerical.estimation.R1ToR1Estimator
org.drip.specialfunction.gamma.StirlingSeries
Direct Known Subclasses:
RobbinsExtension
public class StirlingSeries
extends R1ToR1Estimator
StirlingSeries implements the Stirling's Series Approximation of the Gamma Functions. The References are:
  • Mortici, C. (2011): Improved Asymptotic Formulas for the Gamma Function Computers and Mathematics with Applications 61 (11) 3364-3369
  • National Institute of Standards and Technology (2018): NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/5.11
  • Nemes, G. (2010): On the Coefficients of the Asymptotic Expansion of n! https://arxiv.org/abs/1003.2907 arXiv
  • Toth V. T. (2016): Programmable Calculators – The Gamma Function http://www.rskey.org/CMS/index.php/the-library/11
  • Wikipedia (2019): Stirling's Approximation https://en.wikipedia.org/wiki/Stirling%27s_approximation
It provides the following functionality:
  • StirlingSeries Constructor
  • Compute the de-Moivre Term
  • Compute the Bounded Function Estimates along with the First Order Laplace Correction
  • Compute the Bounded Function Estimates along with the Higher Order Nemes Correction

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

  • Constructor Details

    • StirlingSeries

      public StirlingSeries​(DerivativeControl derivativeControl)
      StirlingSeries Constructor
      Parameters:
      derivativeControl - The Derivative Control

  • Method Details

    • deMoivreTerm

      public double deMoivreTerm​(double x) throws java.lang.Exception
      Compute the de-Moivre Term
      Parameters:
      x - X
      Returns:
      The de-Moivre Term
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • evaluate

      public double evaluate​(double x) throws java.lang.Exception
      Description copied from class: R1ToR1
      Evaluate for the given variate
      Specified by:
      evaluate in class R1ToR1
      Parameters:
      x - Variate
      Returns:
      Returns the calculated value
      Throws:
      java.lang.Exception - Thrown if evaluation cannot be done

    • boundedEstimate

      public R1Estimate boundedEstimate​(double x)
      Description copied from class: R1ToR1Estimator
      Estimate a Bounded Numerical Approximation of the Function Value
      Overrides:
      boundedEstimate in class R1ToR1Estimator
      Parameters:
      x - X
      Returns:
      The Bounded Numerical Approximation

    • laplaceCorrectionEstimate

      public R1Estimate laplaceCorrectionEstimate​(double x)
      Compute the Bounded Function Estimates along with the First Order Laplace Correction
      Parameters:
      x - X
      Returns:
      The Bounded Function Estimates along with the First Order Laplace Correction

    • nemesCorrectionEstimate

      public R1Estimate nemesCorrectionEstimate​(double x)
      Compute the Bounded Function Estimates along with the Higher Order Nemes Correction
      Parameters:
      x - X
      Returns:
      The Bounded Function Estimates along with the Higher Order Nemes Correction