Package org.drip.specialfunction.incompletegamma

Class LowerSFixedSeries

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.RkToR1Series

org.drip.numerical.estimation.R1ToR1Series

org.drip.specialfunction.incompletegamma.LowerSFixedSeries

public class LowerSFixedSeries
extends R1ToR1Series

LowerSFixedSeries implements Lower Incomplete Gamma Expansion Series. 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 R¹ To R¹ Weierstrass Limit Series
• Construct the R¹ To R¹ NIST (2019) Limit Series
• LowerSFixedSeries Constructor
• Retrieve s
• Retrieve Log (Gamma (s))

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
LowerSFixedSeries(R1ToR1SeriesTerm r1ToR1SeriesTerm, java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap, double s, double logGammaS)	LowerSFixedSeries Constructor

Method Summary

Modifier and Type	Method	Description
double	logGammaS()	Retrieve Log (Gamma (s))
static LowerSFixedSeries	NIST2019(double s, int termCount)	Construct the R1 To R1 NIST (2019) Limit Series
double	s()	Retrieve s
static LowerSFixedSeries	WeierstrassLimit(double s, int termCount)	Construct the R1 To R1 Weierstrass Limit Series

Methods inherited from class org.drip.numerical.estimation.R1ToR1Series

cumulative, derivative, evaluate, generate, r1ToR1SeriesTerm

Methods inherited from class org.drip.numerical.estimation.RkToR1Series

proportional, termWeightMap

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

antiDerivative, conditionNumber, 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

LowerSFixedSeries

public LowerSFixedSeries(R1ToR1SeriesTerm r1ToR1SeriesTerm,
java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap,
double s,
double logGammaS)
                  throws java.lang.Exception

LowerSFixedSeries Constructor

Parameters:

r1ToR1SeriesTerm - R¹ To R¹ Series Expansion Term

termWeightMap - Error Term Weight Map

s - s

logGammaS - Log (Gamma (s))

Throws:

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

Method Details

WeierstrassLimit

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

Construct the R¹ To R¹ Weierstrass Limit Series

Parameters:

s - Incomplete Gamma s

termCount - Count of the Number of Terms

Returns:

The R¹ To R¹ Weierstrass Limit Series

NIST2019

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

Construct the R¹ To R¹ NIST (2019) Limit Series

Parameters:

s - Incomplete Gamma s

termCount - Count of the Number of Terms

Returns:

The R¹ To R¹ NIST (2019) Limit Series

s

public double s()

Retrieve s

Returns:

s

logGammaS

public double logGammaS()

Retrieve Log (Gamma (s))

Returns:

Log (Gamma (s))