WindschitlTothAnalytic

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.R1ToR1Estimator

org.drip.specialfunction.gamma.WindschitlTothAnalytic

public class WindschitlTothAnalytic
extends R1ToR1Estimator

WindschitlTothAnalytic implements the Windschitl-Toth Analytic Approximation of the Gamma Function. 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:

WindschitlTothAnalytic Constructor

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

Author:: Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor Description

WindschitlTothAnalytic(DerivativeControl derivativeControl)
WindschitlTothAnalytic Constructor
Method Summary

Modifier and Type Method Description

double evaluate(double x)
Evaluate for the given variate

Methods inherited from class org.drip.numerical.estimation.R1ToR1Estimator
boundedEstimate, seriesEstimate, seriesEstimateNative

Methods inherited from class org.drip.function.definition.R1ToR1
antiDerivative, conditionNumber, derivative, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- WindschitlTothAnalytic
  
  public WindschitlTothAnalytic(DerivativeControl derivativeControl)
  
  WindschitlTothAnalytic Constructor
  
  Parameters:
  
  derivativeControl - The Derivative Control
Method Details
- 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