Package org.drip.specialfunction.derived

Class Jacobi

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.specialfunction.definition.HypergeometricEstimator

org.drip.specialfunction.definition.JacobiEstimator

org.drip.specialfunction.derived.Jacobi

public class Jacobi
extends JacobiEstimator

Jacobi implements the Jacobian 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:

• Jacobi Constructor
• Retrieve the 2F1 Hyper-geometric Function 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
Jacobi(double alpha, double beta, int n, R2ToR1 logBetaEstimator, int quadratureCount)	Jacobi Constructor

Method Summary

Modifier and Type	Method	Description
double	jacobi(double z)	Evaluate The Jacobi Function
RegularHypergeometricEstimator	regularHypergeometricEstimator()	Retrieve the 2F1 Hyper-geometric Function Estimator

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

alpha, beta, evaluate, n

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

Jacobi

public Jacobi(double alpha,
double beta,
int n,
R2ToR1 logBetaEstimator,
int quadratureCount)
       throws java.lang.Exception

Jacobi Constructor

Parameters:

alpha - Alpha

beta - Beta

n - N

logBetaEstimator - Log Beta Estimator

quadratureCount - Quadrature Count

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

jacobi

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

Description copied from class: JacobiEstimator

Evaluate The Jacobi Function

Specified by:

jacobi in class JacobiEstimator

Parameters:

z - Z

Returns:

The Jacobi Function Value

Throws:

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