Package org.drip.specialfunction.incompletegamma

Class LowerSFixed

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.R1ToR1Estimator

org.drip.specialfunction.incompletegamma.LowerSFixed

public abstract class LowerSFixed
extends R1ToR1Estimator

LowerSFixed implements the Lower Incomplete Gamma Function using Power Series for a Fixed 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:

• Construct the Weierstrass Lower S Fixed Series Incomplete Gamma Estimator
• Construct the NIST (2019) Lower S Fixed Series Incomplete Gamma Estimator
• LowerSFixed Constructor
• Compute the Limiting Weierstrass Sum
• Compute the Non-dimensional Incomplete Gamma (Weierstrass Gamma Star)

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
LowerSFixed(LowerSFixedSeries lowerSFixedSeries, DerivativeControl derivativeControl)	LowerSFixed Constructor

Method Summary

Modifier and Type	Method	Description
double	evaluate(double z)	Evaluate for the given variate
static LowerSFixed	NIST2019(double s, int termCount)	Construct the NIST (2019) Lower S Fixed Series Incomplete Gamma Estimator
abstract double	nonDimensional(double z)	Compute the Non-dimensional Incomplete Gamma (Weierstrass Gamma Star)
R1Estimate	seriesEstimateNative(double x)	Compute the Built-in Higher Order Series Estimates
double	weierstrassLimit(double z)	Compute the Limiting Weierstrass Sum
static LowerSFixed	WeierstrassLimit(double s, int termCount)	Construct the Weierstrass Lower S Fixed Series Incomplete Gamma Estimator

Methods inherited from class org.drip.numerical.estimation.R1ToR1Estimator

boundedEstimate, seriesEstimate

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

antiDerivative, conditionNumber, derivative, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

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

Constructor Details

LowerSFixed

public LowerSFixed(LowerSFixedSeries lowerSFixedSeries,
DerivativeControl derivativeControl)
            throws java.lang.Exception

LowerSFixed Constructor

Parameters:

lowerSFixedSeries - R¹ To R¹ Lower S Fixed Limit Series

derivativeControl - Differential Control

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

WeierstrassLimit

public static final LowerSFixed WeierstrassLimit(double s,
int termCount)

Construct the Weierstrass Lower S Fixed Series Incomplete Gamma Estimator

Parameters:

s - Incomplete Gamma s

termCount - Count of the Number of Terms

Returns:

The Weierstrass Lower S Fixed Series Incomplete Gamma Estimator

NIST2019

public static final LowerSFixed NIST2019(double s,
int termCount)

Construct the NIST (2019) Lower S Fixed Series Incomplete Gamma Estimator

Parameters:

s - Incomplete Gamma s

termCount - Count of the Number of Terms

Returns:

The NIST (2019) Lower S Fixed Series Incomplete Gamma Estimator

seriesEstimateNative

public R1Estimate seriesEstimateNative(double x)

Description copied from class: R1ToR1Estimator

Compute the Built-in Higher Order Series Estimates

Overrides:

seriesEstimateNative in class R1ToR1Estimator

Parameters:

x - X

Returns:

The Built-in Higher Order Series Estimates

weierstrassLimit

public double weierstrassLimit(double z)
                        throws java.lang.Exception

Compute the Limiting Weierstrass Sum

Parameters:

z - Z

Returns:

The Limiting Weierstrass Sum

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

nonDimensional

public abstract double nonDimensional(double z)
                               throws java.lang.Exception

Compute the Non-dimensional Incomplete Gamma (Weierstrass Gamma Star)

Parameters:

z - Z

Returns:

The Non-dimensional Incomplete Gamma (Weierstrass Gamma Star)

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

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