Package org.drip.specialfunction.incompletegamma

Class UpperRegularized

java.lang.Object
org.drip.specialfunction.incompletegamma.UpperRegularized
public abstract class UpperRegularized
extends java.lang.Object
UpperRegularized implements the Regularized Version of the Upper Incomplete Gamma. 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:
  • Construct the Gauss Continued Version of Upper Regularized Incomplete Gamma Function
  • Construct the Abramowitz Stegun 2007 Version of Upper Regularized Incomplete Gamma Function
  • Construct the Euler Integral Version of Upper Regularized Incomplete Gamma Function
  • Construct the Weisstein Version of Upper Regularized Incomplete Gamma Function
  • Compute p (s, z)

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

  • Method Summary

    Modifier and Type Method Description
    static UpperRegularized AbramowitzStegun2007​(int n)
    Construct the Abramowitz Stegun 2007 Version of Upper Regularized Incomplete Gamma Function
    static UpperRegularized EulerIntegral()
    Construct the Euler Integral Version of Upper Regularized Incomplete Gamma Function
    static UpperRegularized GaussContinuedFraction​(int n)
    Construct the Gauss Continued Version of Upper Regularized Incomplete Gamma Function
    abstract double p​(double s, double z)
    Compute p (s, z)
    static UpperRegularized Weisstein()
    Construct the Weisstein Version of Upper Regularized Incomplete Gamma Function

    Methods inherited from class java.lang.Object

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

  • Method Details

    • GaussContinuedFraction

      public static final UpperRegularized GaussContinuedFraction​(int n)
      Construct the Gauss Continued Version of Upper Regularized Incomplete Gamma Function
      Parameters:
      n - Count of the Number of Terms
      Returns:
      Gauss Continued Version of Upper Regularized Incomplete Gamma Function

    • AbramowitzStegun2007

      public static final UpperRegularized AbramowitzStegun2007​(int n)
      Construct the Abramowitz Stegun 2007 Version of Upper Regularized Incomplete Gamma Function
      Parameters:
      n - Count of the Number of Terms
      Returns:
      Abramowitz Stegun 2007 Version of Upper Regularized Incomplete Gamma Function

    • EulerIntegral

      public static final UpperRegularized EulerIntegral()
      Construct the Euler Integral Version of Upper Regularized Incomplete Gamma Function
      Returns:
      Euler Integral Version of Upper Regularized Incomplete Gamma Function

    • Weisstein

      public static final UpperRegularized Weisstein()
      Construct the Weisstein Version of Upper Regularized Incomplete Gamma Function
      Returns:
      Weisstein Version of Upper Regularized Incomplete Gamma Function

    • p

      public abstract double p​(double s, double z) throws java.lang.Exception
      Compute p (s, z)
      Parameters:
      s - s
      z - z
      Returns:
      p(s, z)
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid