Package org.drip.specialfunction.hypergeometric

Class EulerQuadratureEstimator

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.specialfunction.definition.HypergeometricEstimator
org.drip.specialfunction.definition.RegularHypergeometricEstimator
org.drip.specialfunction.hypergeometric.EulerQuadratureEstimator
public class EulerQuadratureEstimator
extends RegularHypergeometricEstimator
EulerQuadratureEstimator estimates the Hyper-geometric Function using the Euler Integral Representation. 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:
  • EulerQuadratureEstimator Constructor
  • Retrieve the Quadrature Count
  • Retrieve the Log Beta Estimator

Module Computational Core Module
Library Function Analysis Library
Project Special Function Implementation and Analysis
Package Hyper-geometric Function Estimation Schemes
Author:
Lakshmi Krishnamurthy

  • Constructor Details

    • EulerQuadratureEstimator

      public EulerQuadratureEstimator​(HypergeometricParameters hypergeometricParameters, R2ToR1 logBetaEstimator, int quadratureCount) throws java.lang.Exception
      EulerQuadratureEstimator Constructor
      Parameters:
      hypergeometricParameters - Hyper-geometric Parameters
      logBetaEstimator - Log Beta Estimator
      quadratureCount - Count of the Integrand Quadrature
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • quadratureCount

      public int quadratureCount()
      Retrieve the Quadrature Count
      Returns:
      The Quadrature Count

    • logBetaEstimator

      public R2ToR1 logBetaEstimator()
      Retrieve the Log Beta Estimator
      Returns:
      The Log Beta Estimator

    • regularHypergeometric

      public double regularHypergeometric​(double z) throws java.lang.Exception
      Description copied from class: RegularHypergeometricEstimator
      Evaluate Regular Hyper-geometric Function
      Specified by:
      regularHypergeometric in class RegularHypergeometricEstimator
      Parameters:
      z - Z
      Returns:
      Regular Hyper-geometric Value
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • derivative

      public double derivative​(double z, int order) throws java.lang.Exception
      Description copied from class: R1ToR1
      Calculate the derivative as a double
      Overrides:
      derivative in class R1ToR1
      Parameters:
      z - Variate at which the derivative is to be calculated
      order - Order of the derivative to be computed
      Returns:
      The Derivative
      Throws:
      java.lang.Exception - Thrown if Inputs are Invalid

    • albinate

      public RegularHypergeometricEstimator albinate​(HypergeometricParameters hypergeometricParametersAlbinate, R1ToR1 valueScaler, R1ToR1 zTransformer)
      Description copied from class: RegularHypergeometricEstimator
      Albinate (i.e., Clone + Mutate) an Instance of Regular Hyper-geometric Estimator
      Specified by:
      albinate in class RegularHypergeometricEstimator
      Parameters:
      hypergeometricParametersAlbinate - The Albination Hyper-geometric Parameters
      valueScaler - The Estimator Value Scaler
      zTransformer - The Z Transformation Function
      Returns:
      Albinated Instance of Regular Hyper-geometric Estimator