Package org.drip.specialfunction.bessel

Class ModifiedSecondIntegralEstimator

java.lang.Object

org.drip.specialfunction.definition.ModifiedBesselSecondKindEstimator

org.drip.specialfunction.bessel.ModifiedSecondIntegralEstimator

All Implemented Interfaces:

R2ToR1

public abstract class ModifiedSecondIntegralEstimator
extends ModifiedBesselSecondKindEstimator

ModifiedSecondIntegralEstimator implements the Integral Estimator for the Modified Bessel Function of the Second Kind. The References are:

• Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
• Arfken, G. B., and H. J. Weber (2005): Mathematical Methods for Physicists 6^th Edition Harcourt San Diego
• Temme N. M. (1996): Special Functions: An Introduction to the Classical Functions of Mathematical Physics 2^nd Edition Wiley New York
• Watson, G. N. (1995): A Treatise on the Theory of Bessel Functions Cambridge University Press
• Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_function

It provides the following functionality:

• Construct the Modified Bessel Second Kind Estimator from the Integral Form
• Construct the Modified Bessel Second Kind Zero Order Estimator from the Integral Form
• Construct the Modified Bessel Second Kind Estimator for the 1. / 3. Order from the Integral Form
• Construct the Modified Bessel Second Kind Estimator for the 2. / 3. Order from the Integral Form
• Retrieve the Quadrature Count

Module	Product Core Module
Library	Fixed Income Analytics
Project	Special Function Implementation and Analysis
Package	Ordered Bessel Function Variant Estimators

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
static ModifiedSecondIntegralEstimator	OneThirdOrder(int quadratureCount)	Construct the Modified Bessel Second Kind Estimator for the 1.
int	quadratureCount()	Retrieve the Quadrature Count
static ModifiedSecondIntegralEstimator	Standard(int quadratureCount)	Construct the Modified Bessel Second Kind Estimator from the Integral Form
static ModifiedSecondIntegralEstimator	TwoThirdOrder(int quadratureCount)	Construct the Modified Bessel Second Kind Estimator for the 2.
static ModifiedSecondIntegralEstimator	ZeroOrder(int quadratureCount)	Construct the Modified Bessel Second Kind Zero Order Estimator from the Integral Form

Methods inherited from class org.drip.specialfunction.definition.ModifiedBesselSecondKindEstimator

AlphaStrictlyPositiveAsymptote, AlphaZeroAsymptote, bigK, evaluate

Methods inherited from class java.lang.Object

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

Method Details

Standard

public static final ModifiedSecondIntegralEstimator Standard(int quadratureCount)

Construct the Modified Bessel Second Kind Estimator from the Integral Form

Parameters:

quadratureCount - Count of the Integrand Quadrature

Returns:

Modified Bessel Second Kind Estimator from the Integral Form

ZeroOrder

public static final ModifiedSecondIntegralEstimator ZeroOrder(int quadratureCount)

Construct the Modified Bessel Second Kind Zero Order Estimator from the Integral Form

Parameters:

quadratureCount - Count of the Integrand Quadrature

Returns:

Modified Bessel Second Kind Zero Order Estimator from the Integral Form

OneThirdOrder

public static final ModifiedSecondIntegralEstimator OneThirdOrder(int quadratureCount)

Construct the Modified Bessel Second Kind Estimator for the 1. / 3. Order from the Integral Form

Parameters:

quadratureCount - Count of the Integrand Quadrature

Returns:

Modified Bessel Second Kind Estimator for the 1. / 3. Order from the Integral Form

TwoThirdOrder

public static final ModifiedSecondIntegralEstimator TwoThirdOrder(int quadratureCount)

Construct the Modified Bessel Second Kind Estimator for the 2. / 3. Order from the Integral Form

Parameters:

quadratureCount - Count of the Integrand Quadrature

Returns:

Modified Bessel Second Kind Estimator for the 2. / 3. Order from the Integral Form

quadratureCount

public int quadratureCount()

Retrieve the Quadrature Count

Returns:

The Quadrature Count