Package org.drip.specialfunction.gamma

Class RobbinsExtension

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.numerical.estimation.R1ToR1Estimator
org.drip.specialfunction.gamma.StirlingSeries
org.drip.specialfunction.gamma.RobbinsExtension
public class RobbinsExtension
extends StirlingSeries
RobbinsExtension implements the Robbins (1955) Extension of the Stirling's 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:
  • RobbinsExtension 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 Details

    • RobbinsExtension

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

  • Method Details

    • boundedEstimate

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