Package org.drip.specialfunction.incompletegamma

Class LimitAsymptote

java.lang.Object
org.drip.specialfunction.incompletegamma.LimitAsymptote
public abstract class LimitAsymptote
extends java.lang.Object
LimitAsymptote implements the Asymptotes 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:
  • Construct the Lower Incomplete Gamma Asymptote Function
  • Construct the Upper Incomplete Gamma Asymptote Function
  • Retrieve the z tends to Zero Asymptote
  • Retrieve the z tends to Infinity Asymptote

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 LimitAsymptote Lower()
    Construct the Lower Incomplete Gamma Asymptote Function
    static LimitAsymptote Upper()
    Construct the Upper Incomplete Gamma Asymptote Function
    abstract R1ToR1 zInfinity​(double s)
    Retrieve the z tends to Infinity Asymptote
    abstract R1ToR1 zZero​(double s)
    Retrieve the z tends to Zero Asymptote

    Methods inherited from class java.lang.Object

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

  • Method Details

    • Lower

      public static final LimitAsymptote Lower()
      Construct the Lower Incomplete Gamma Asymptote Function
      Returns:
      The Lower Incomplete Gamma Asymptote Function

    • Upper

      public static final LimitAsymptote Upper()
      Construct the Upper Incomplete Gamma Asymptote Function
      Returns:
      The Upper Incomplete Gamma Asymptote Function

    • zZero

      public abstract R1ToR1 zZero​(double s)
      Retrieve the z tends to Zero Asymptote
      Parameters:
      s - s
      Returns:
      The z tends to Zero Asymptote

    • zInfinity

      public abstract R1ToR1 zInfinity​(double s)
      Retrieve the z tends to Infinity Asymptote
      Parameters:
      s - s
      Returns:
      The z tends to Infinity Asymptote