Package org.drip.specialfunction.bessel

Class ModifiedFirstFrobeniusSeriesEstimator

java.lang.Object
org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
org.drip.specialfunction.bessel.ModifiedFirstFrobeniusSeriesEstimator
All Implemented Interfaces:
R2ToR1
public class ModifiedFirstFrobeniusSeriesEstimator
extends ModifiedBesselFirstKindEstimator
ModifiedFirstFrobeniusSeriesEstimator implements the Frobenius Series Estimator for the Modified 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 a Standard Instance of Bessel ModifiedFirstFrobeniusSeriesEstimator
  • Retrieve the Frobenius Series

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

  • Method Details

    • Standard

      public static final ModifiedFirstFrobeniusSeriesEstimator Standard​(R1ToR1 gammaEstimator, int termCount)
      Construct a Standard Instance of Bessel ModifiedFirstFrobeniusSeriesEstimator
      Parameters:
      gammaEstimator - The Gamma Estimator
      termCount - Count of the Number of Terms
      Returns:
      The Standard Instance of Bessel ModifiedFirstFrobeniusSeriesEstimator

    • frobeniusSeries

      public R2ToR1Series frobeniusSeries()
      Retrieve the Frobenius Series
      Returns:
      The Frobenius Series

    • bigI

      public double bigI​(double alpha, double z) throws java.lang.Exception
      Description copied from class: ModifiedBesselFirstKindEstimator
      Evaluate Modified Bessel Function First Kind I given Alpha and z
      Specified by:
      bigI in class ModifiedBesselFirstKindEstimator
      Parameters:
      alpha - Alpha
      z - Z
      Returns:
      Modified Bessel Function First Kind I Value
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid