Package org.drip.specialfunction.hypergeometric

Class PochhammerSeriesTerm

java.lang.Object

org.drip.numerical.estimation.R1ToR1SeriesTerm

org.drip.specialfunction.hypergeometric.PochhammerSeriesTerm

public class PochhammerSeriesTerm
extends R1ToR1SeriesTerm

PochhammerSeriesTerm refers to a Single Series Term in the Pochhammer Series Expansion of the 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:

• PochhammerSeriesTerm Constructor
• Retrieve the Hyper-geometric Parameters

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

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
PochhammerSeriesTerm(HypergeometricParameters hypergeometricParameters)	PochhammerSeriesTerm Constructor

Method Summary

Modifier and Type	Method	Description
HypergeometricParameters	hypergeometricParameters()	Retrieve the Hyper-geometric Parameters
double	value(int order, double z)	Compute the Value of the R1 To R1 Series Expansion Term

Methods inherited from class org.drip.numerical.estimation.R1ToR1SeriesTerm

Asymptotic, derivative, InvertedRisingExponential, Taylor

Methods inherited from class java.lang.Object

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

Constructor Details

PochhammerSeriesTerm

public PochhammerSeriesTerm(HypergeometricParameters hypergeometricParameters)
                     throws java.lang.Exception

PochhammerSeriesTerm Constructor

Parameters:

hypergeometricParameters - The Hyper-geometric Parameters

Throws:

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

Method Details

hypergeometricParameters

public HypergeometricParameters hypergeometricParameters()

Retrieve the Hyper-geometric Parameters

Returns:

The Hyper-geometric Parameters

value

public double value(int order,
double z)
             throws java.lang.Exception

Description copied from class: R1ToR1SeriesTerm

Compute the Value of the R¹ To R¹ Series Expansion Term

Specified by:

value in class R1ToR1SeriesTerm

Parameters:

order - Order of the R¹ To R¹ Series Expansion Term

z - X

Returns:

The Value of the R¹ To R¹ Series Expansion Term

Throws:

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