Package org.drip.specialfunction.incompletegamma

Class LowerLimitPowerIntegrand

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.specialfunction.incompletegamma.LowerLimitPowerIntegrand
public class LowerLimitPowerIntegrand
extends R1ToR1
LowerLimitPowerIntegrand contains the Integrand that is the Product of the Limit raised to a Power Exponent and the corresponding Lower Incomplete Gamma, for a given s. 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:
  • LowerLimitPowerIntegrand Constructor
  • Retrieve s
  • Retrieve the Limit Power Exponent

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
    LowerLimitPowerIntegrand​(DerivativeControl derivativeControl, double s, double limitExponent)
    LowerLimitPowerIntegrand Constructor

  • Method Summary

    Modifier and Type Method Description
    R1ToR1 antiDerivative()
    Compute the Anti-Derivative Function
    double evaluate​(double z)
    Evaluate for the given variate
    double integrate​(double left, double right)
    Integrate over the given range
    double limitExponent()
    Retrieve the Limit Power Exponent
    double s()
    Retrieve s

    Methods inherited from class org.drip.function.definition.R1ToR1

    derivative, differential, differential, maxima, maxima, minima, minima, poleResidue

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • LowerLimitPowerIntegrand

      public LowerLimitPowerIntegrand​(DerivativeControl derivativeControl, double s, double limitExponent) throws java.lang.Exception
      LowerLimitPowerIntegrand Constructor
      Parameters:
      derivativeControl - The Derivative Control
      s - s
      limitExponent - The Limit Power Exponent
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • s

      public double s()
      Retrieve s
      Returns:
      s

    • limitExponent

      public double limitExponent()
      Retrieve the Limit Power Exponent
      Returns:
      The Limit Power Exponent

    • evaluate

      public double evaluate​(double z) throws java.lang.Exception
      Description copied from class: R1ToR1
      Evaluate for the given variate
      Specified by:
      evaluate in class R1ToR1
      Parameters:
      z - Variate
      Returns:
      Returns the calculated value
      Throws:
      java.lang.Exception - Thrown if evaluation cannot be done

    • antiDerivative

      public R1ToR1 antiDerivative()
      Description copied from class: R1ToR1
      Compute the Anti-Derivative Function
      Overrides:
      antiDerivative in class R1ToR1
      Returns:
      The Anti-Derivative Function

    • integrate

      public double integrate​(double left, double right) throws java.lang.Exception
      Description copied from class: R1ToR1
      Integrate over the given range
      Overrides:
      integrate in class R1ToR1
      Parameters:
      left - Range Begin
      right - Range End
      Returns:
      The Integrated Value
      Throws:
      java.lang.Exception - Thrown if evaluation cannot be done