Package org.drip.specialfunction.definition

Class LegendreEstimator

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.specialfunction.definition.HypergeometricEstimator
org.drip.specialfunction.definition.LegendreEstimator
Direct Known Subclasses:
Legendre
public abstract class LegendreEstimator
extends HypergeometricEstimator
LegendreEstimator exposes the Stubs for estimating the Legendre Function and its Jacobian using the 2F1 Hyper-geometric Function. The References are:

  • Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series SIAM Journal on Mathematical Analysis 13 (2) 295-308
  • Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation Journal of Symbolic Computation 20 (4) 399-417
  • Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the Sum of a (_2^3)F(a,b;c;z) Journal of Computational and Applied Mathematics 72 293-300
  • National Institute of Standards and Technology (2019): Hyper-geometric Function https://dlmf.nist.gov/15
  • Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_function
It provides the following functionality:
  • Retrieve Legendre Alpha
  • Retrieve Legendre Ceta
  • Evaluate the Legendre Function

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

  • Method Details

    • alpha

      public double alpha()
      Retrieve Legendre Alpha
      Returns:
      The Legendre Alpha

    • ceta

      public double ceta()
      Retrieve Legendre Ceta
      Returns:
      The Legendre Ceta

    • evaluate

      public double evaluate​(double z) throws java.lang.Exception
      Description copied from class: R1ToR1
      Evaluate for the given variate
      Specified by:
      evaluate in class R1ToR1
      Parameters:
      z - Variate
      Returns:
      Returns the calculated value
      Throws:
      java.lang.Exception - Thrown if evaluation cannot be done

    • legendre

      public abstract double legendre​(double z) throws java.lang.Exception
      Evaluate the Legendre Function
      Parameters:
      z - Z
      Returns:
      The Legendre Function Value
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid