Package org.drip.specialfunction.definition

Class BesselFirstKindEstimator

java.lang.Object
org.drip.specialfunction.definition.BesselFirstKindEstimator
All Implemented Interfaces:
R2ToR1
Direct Known Subclasses:
FirstFrobeniusSeriesEstimator, FirstSchlafliIntegralEstimator
public abstract class BesselFirstKindEstimator
extends java.lang.Object
implements R2ToR1
BesselFirstKindEstimator exposes the Estimator for the Bessel Function of the First 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 Positive Integer Asymptotic Version of BesselFirstKindEstimator
  • Construct the Alpha Negative Integer Asymptotic Version of BesselFirstKindEstimator
  • Construct the High z Asymptotic Version of BesselFirstKindEstimator
  • Construct the Alpha = 0 Negative z Asymptotic Version of BesselFirstKindEstimator
  • Construct the Approximate Zero Alpha Bessel Estimator of the First Kind
  • Evaluate Bessel Function First Kind J 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

    • BesselFirstKindEstimator

      public BesselFirstKindEstimator()

  • Method Details

    • AlphaPositiveIntegerOrZeroAsymptote

      public static final BesselFirstKindEstimator AlphaPositiveIntegerOrZeroAsymptote​(R1ToR1 gammaEstimator)
      Construct the Alpha Positive Integer or Zero Asymptotic Version of BesselFirstKindEstimator
      Parameters:
      gammaEstimator - Gamma Estimator
      Returns:
      Alpha Positive Integer or Zero Asymptotic Version of BesselFirstKindEstimator

    • AlphaNegativeIntegerAsymptote

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

    • HighZAsymptote

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

    • AlphaZeroNegativeZAsymptote

      public static final BesselFirstKindEstimator AlphaZeroNegativeZAsymptote()
      Construct the Alpha = 0 Negative z Asymptotic Version of BesselFirstKindEstimator
      Returns:
      Alpha = 0 Negative z Asymptotic Version of BesselFirstKindEstimator

    • AlphaZeroApproximate

      public static final BesselFirstKindEstimator AlphaZeroApproximate()
      Construct the Approximate Zero Alpha Bessel Estimator of the First Kind
      Returns:
      The Approximate Zero Alpha Bessel Estimator of the First Kind

    • bigJ

      public abstract double bigJ​(double alpha, double z) throws java.lang.Exception
      Evaluate Bessel Function First Kind J given Alpha and z
      Parameters:
      alpha - Alpha
      z - Z
      Returns:
      Bessel Function First Kind J 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