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 e^iÏ€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

conditionNumber, 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