Package org.drip.specialfunction.bessel

Class SecondNISTSeriesEstimator

java.lang.Object

org.drip.specialfunction.definition.BesselSecondKindEstimator

org.drip.specialfunction.bessel.SecondNISTSeriesEstimator

All Implemented Interfaces:

R2ToR1

public class SecondNISTSeriesEstimator
extends BesselSecondKindEstimator

SecondNISTSeriesEstimator implements the NIST Series Estimator for the Cylindrical 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 a Standard Instance of SecondNISTSeriesEstimator
• Retrieve the Bessel Second Kind NIST Series
• Retrieve the Bessel Function First Kind Estimator

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
BesselFirstKindEstimator	besselFirstKindEstimator()	Retrieve the Bessel Function First Kind Estimator
R2ToR1Series	besselSecondKindNISTSeries()	Retrieve the Bessel Second Kind NIST Series
double	bigY(double alpha, double z)	Evaluate Bessel Function Second Kind Y given Alpha and z
static SecondNISTSeriesEstimator	Standard(R1ToR1 digammaEstimator, R1ToR1 gammaEstimator, BesselFirstKindEstimator besselFirstKindEstimator, int termCount)	Construct a Standard Instance of SecondNISTSeriesEstimator

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

AlphaNegativeIntegerAsymptote, AlphaNonNegativeIntegerAsymptote, AlphaZeroAsymptote, evaluate, HighZAsymptote

Methods inherited from class java.lang.Object

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

Method Details

Standard

public static final SecondNISTSeriesEstimator Standard(R1ToR1 digammaEstimator,
R1ToR1 gammaEstimator,
BesselFirstKindEstimator besselFirstKindEstimator,
int termCount)

Construct a Standard Instance of SecondNISTSeriesEstimator

Parameters:

digammaEstimator - The Digamma Estimator

gammaEstimator - The Gamma Estimator

besselFirstKindEstimator - The Bessel Function First Kind Estimator

termCount - Count of the Number of Terms

Returns:

The Standard Instance of SecondNISTSeriesEstimator

besselSecondKindNISTSeries

public R2ToR1Series besselSecondKindNISTSeries()

Retrieve the Bessel Second Kind NIST Series

Returns:

The Bessel Second Kind NIST Series

besselFirstKindEstimator

public BesselFirstKindEstimator besselFirstKindEstimator()

Retrieve the Bessel Function First Kind Estimator

Returns:

The Bessel Function First Kind Estimator

bigY

public double bigY(double alpha,
double z)
            throws java.lang.Exception

Description copied from class: BesselSecondKindEstimator

Evaluate Bessel Function Second Kind Y given Alpha and z

Specified by:

bigY in class BesselSecondKindEstimator

Parameters:

alpha - Alpha

z - Z

Returns:

Bessel Function Second Kind Y Value

Throws:

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