Package org.drip.specialfunction.incompletegamma

Class LowerRegularized

java.lang.Object
org.drip.specialfunction.incompletegamma.LowerRegularized
public abstract class LowerRegularized
extends java.lang.Object
LowerRegularized implements the Regularized Version of the Lower 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 Fraction Version of Lower Regularized Incomplete Gamma Function
  • Construct the Euler Integral Version of Lower Regularized Incomplete Gamma Function
  • Construct the Weierstrass Version of Lower Regularized Incomplete Gamma Function
  • Construct the NIST (2019) Version of Lower 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 LowerRegularized EulerIntegral()
    Construct the Euler Integral Version of Lower Regularized Incomplete Gamma Function
    static LowerRegularized GaussContinuedFraction​(int n)
    Construct the Gauss Continued Fraction Version of Lower Regularized Incomplete Gamma Function
    static LowerRegularized NIST2019​(int n)
    Construct the NIST (2019) Version of Lower Regularized Incomplete Gamma Function
    abstract double p​(double s, double z)
    Compute p (s, z)
    static LowerRegularized WeierstrassLimit​(int n)
    Construct the Weierstrass Limit Version of Lower 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 LowerRegularized GaussContinuedFraction​(int n)
      Construct the Gauss Continued Fraction Version of Lower Regularized Incomplete Gamma Function
      Parameters:
      n - Count of the Number of Terms
      Returns:
      Gauss Continued Version of Lower Regularized Incomplete Gamma Function

    • EulerIntegral

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

    • WeierstrassLimit

      public static final LowerRegularized WeierstrassLimit​(int n)
      Construct the Weierstrass Limit Version of Lower Regularized Incomplete Gamma Function
      Parameters:
      n - Count of the Number of Terms
      Returns:
      Weierstrass Limit Version of Lower Regularized Incomplete Gamma Function

    • NIST2019

      public static final LowerRegularized NIST2019​(int n)
      Construct the NIST (2019) Version of Lower Regularized Incomplete Gamma Function
      Parameters:
      n - Count of the Number of Terms
      Returns:
      NIST (2019) Version of Lower 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