Package org.drip.specialfunction.derived

Class Legendre

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.specialfunction.definition.HypergeometricEstimator

org.drip.specialfunction.definition.LegendreEstimator

org.drip.specialfunction.derived.Legendre

public class Legendre
extends LegendreEstimator

Legendre implements the Legendre Function from 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:

• Legendre Constructor
• Retrieve the 2F1 Hyper-geometric Function Estimator
• Retrieve the Gamma Estimator

Module	Product Core Module
Library	Fixed Income Analytics
Project	Special Function Implementation and Analysis
Package	Special Functions Derived using Others

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
Legendre(double alpha, double ceta, R2ToR1 logBetaEstimator, int quadratureCount, R1ToR1 gammaEstimator)	Legendre Constructor

Method Summary

Modifier and Type	Method	Description
R1ToR1	gammaEstimator()	Retrieve the Gamma Estimator
double	legendre(double z)	Evaluate the Legendre Function
RegularHypergeometricEstimator	regularHypergeometricEstimator()	Retrieve the 2F1 Hyper-geometric Function Estimator

Methods inherited from class org.drip.specialfunction.definition.LegendreEstimator

alpha, ceta, evaluate

Methods inherited from class org.drip.specialfunction.definition.HypergeometricEstimator

hypergeometricParameters

Methods inherited from class org.drip.function.definition.R1ToR1

antiDerivative, conditionNumber, derivative, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Legendre

public Legendre(double alpha,
double ceta,
R2ToR1 logBetaEstimator,
int quadratureCount,
R1ToR1 gammaEstimator)
         throws java.lang.Exception

Legendre Constructor

Parameters:

alpha - Alpha

ceta - Ceta

logBetaEstimator - Log Beta Estimator

quadratureCount - Quadrature Count

gammaEstimator - Gamma Estimator

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

regularHypergeometricEstimator

public RegularHypergeometricEstimator regularHypergeometricEstimator()

Retrieve the 2F1 Hyper-geometric Function Estimator

Returns:

The 2F1 Hyper-geometric Function Estimator

gammaEstimator

public R1ToR1 gammaEstimator()

Retrieve the Gamma Estimator

Returns:

The Gamma Estimator

legendre

public double legendre(double z)
                throws java.lang.Exception

Description copied from class: LegendreEstimator

Evaluate the Legendre Function

Specified by:

legendre in class LegendreEstimator

Parameters:

z - Z

Returns:

The Legendre Function Value

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid