Package org.drip.specialfunction.incompletegamma

Class GaussContinuedFraction

java.lang.Object
org.drip.specialfunction.incompletegamma.GaussContinuedFraction
public class GaussContinuedFraction
extends java.lang.Object
GaussContinuedFraction implements the Gauss Continued Fraction Based Estimates for the Lower/Upper Incomplete Gamma Function. The References are:

  • Geddes, K. O., M. L. Glasser, R. A. Moore, and T. C. Scott (1990): Evaluation of Classes of Definite Integrals involving Elementary Functions via Differentiation of Special Functions Applicable Algebra in Engineering, Communications, and 1 (2) 149-165
  • Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015): Tables of Integrals, Series, and Products Academic Press
  • Mathar, R. J. (2010): Numerical Evaluation of the Oscillatory Integral over eiÏ€x x(1/x) between 1 and ∞ https://arxiv.org/pdf/0912.3844.pdf arXiV
  • National Institute of Standards and Technology (2019): Incomplete Gamma and Related Functions https://dlmf.nist.gov/8
  • Wikipedia (2019): Incomplete Gamma Function https://en.wikipedia.org/wiki/Incomplete_gamma_function
It provides the following functionality:
  • Compute the Lower Incomplete Gamma Function using Gauss Continued Fraction
  • Compute the Upper Incomplete Gamma Function using Abramowitz-Stegun Gauss Continued Fraction
  • Compute the Upper Incomplete Gamma Function using Gauss Continued Fraction

Module Computational Core Module
Library Function Analysis Library
Project Special Function Implementation and Analysis
Package Upper/Lower Incomplete Gamma Functions
Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    GaussContinuedFraction()  

  • Method Summary

    Modifier and Type Method Description
    static double Lower​(double z, double s, int n)
    Compute the Lower Incomplete Gamma Function using the Gauss Continued Fraction
    static double Upper​(double z, double s, int n)
    Compute the Upper Incomplete Gamma Function using Gauss Continued Fraction
    static double UpperAbramowitzStegun2007​(double z, double s, int n)
    Compute the Upper Incomplete Gamma Function using the Abramowitz-Stegun Gauss Continued Fraction

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • GaussContinuedFraction

      public GaussContinuedFraction()

  • Method Details

    • Lower

      public static final double Lower​(double z, double s, int n) throws java.lang.Exception
      Compute the Lower Incomplete Gamma Function using the Gauss Continued Fraction
      Parameters:
      z - z
      s - s
      n - Count of the Number of Terms
      Returns:
      The Lower Incomplete Gamma Function
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • UpperAbramowitzStegun2007

      public static final double UpperAbramowitzStegun2007​(double z, double s, int n) throws java.lang.Exception
      Compute the Upper Incomplete Gamma Function using the Abramowitz-Stegun Gauss Continued Fraction
      Parameters:
      z - z
      s - s
      n - Count of the Number of Terms
      Returns:
      The Upper Incomplete Gamma Function using the Abramowitz-Stegun Gauss Continued Fraction
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • Upper

      public static final double Upper​(double z, double s, int n) throws java.lang.Exception
      Compute the Upper Incomplete Gamma Function using Gauss Continued Fraction
      Parameters:
      z - z
      s - s
      n - Count of the Number of Terms
      Returns:
      The Upper Incomplete Gamma Function using Gauss Continued Fraction
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid