Package org.drip.specialfunction.definition

Class BesselSecondKindEstimator

java.lang.Object
org.drip.specialfunction.definition.BesselSecondKindEstimator
All Implemented Interfaces:
R2ToR1
Direct Known Subclasses:
SecondNISTSeriesEstimator, SecondWatsonIntegralEstimator, SecondWeberEstimator
public abstract class BesselSecondKindEstimator
extends java.lang.Object
implements R2ToR1
BesselSecondKindEstimator exposes the Estimator for the 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 6th Edition Harcourt San Diego
  • Temme N. M. (1996): Special Functions: An Introduction to the Classical Functions of Mathematical Physics 2nd 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 Alpha Zero Asymptotic Version of BesselSecondKindEstimator
  • Construct the Alpha Non-Negative Integer Asymptotic Version of BesselSecondKindEstimator
  • Construct the Alpha Negative Integer Asymptotic Version of BesselSecondKindEstimator
  • Construct the High z Asymptotic Version of BesselSecondKindEstimator
  • Evaluate Bessel Function Second Kind Y given Alpha and z

Module Product Core Module
Library Fixed Income Analytics
Project Special Function Implementation and Analysis
Package Definition of Special Function Estimators
Author:
Lakshmi Krishnamurthy

  • Constructor Details

    • BesselSecondKindEstimator

      public BesselSecondKindEstimator()

  • Method Details

    • AlphaZeroAsymptote

      public static final BesselSecondKindEstimator AlphaZeroAsymptote()
      Construct the Alpha Zero Asymptotic Version of BesselSecondKindEstimator
      Returns:
      Alpha Zero Asymptotic Version of BesselSecondKindEstimator

    • AlphaNonNegativeIntegerAsymptote

      public static final BesselSecondKindEstimator AlphaNonNegativeIntegerAsymptote​(R1ToR1 gammaEstimator)
      Construct the Alpha Non-Negative Integer Asymptotic Version of BesselSecondKindEstimator
      Parameters:
      gammaEstimator - Gamma Estimator
      Returns:
      Alpha Non-Negative Integer Asymptotic Version of BesselSecondKindEstimator

    • AlphaNegativeIntegerAsymptote

      public static final BesselSecondKindEstimator AlphaNegativeIntegerAsymptote​(R1ToR1 gammaEstimator)
      Construct the Alpha Negative Integer Asymptotic Version of BesselSecondKindEstimator
      Parameters:
      gammaEstimator - Gamma Estimator
      Returns:
      Alpha Negative Integer Asymptotic Version of BesselSecondKindEstimator

    • HighZAsymptote

      public static final BesselSecondKindEstimator HighZAsymptote()
      Construct the High z Asymptotic Version of BesselSecondKindEstimator
      Returns:
      High z Asymptotic Version of BesselSecondKindEstimator

    • bigY

      public abstract double bigY​(double alpha, double z) throws java.lang.Exception
      Evaluate Bessel Function Second Kind Y given Alpha and z
      Parameters:
      alpha - Alpha
      z - Z
      Returns:
      Bessel Function Second Kind Y Value
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • evaluate

      public double evaluate​(double alpha, double z) throws java.lang.Exception
      Description copied from interface: R2ToR1
      Evaluate for the given variate Pair
      Specified by:
      evaluate in interface R2ToR1
      Parameters:
      alpha - X
      z - Y
      Returns:
      Returns the calculated value
      Throws:
      java.lang.Exception - Thrown if evaluation cannot be done