Package org.drip.specialfunction.property

Class GammaPolynomialQuotientLemma

java.lang.Object

org.drip.specialfunction.property.GammaPolynomialQuotientLemma

public class GammaPolynomialQuotientLemma
extends java.lang.Object

GammaPolynomialQuotientLemma contains the Verifiable Gamma Polynomial Quotient Equality Lemma. The References are:

• Blagouchine, I. V. (2014): Re-discovery of Malmsten's Integrals, their Evaluation by Contour Integration Methods, and some Related Results Ramanujan Journal 35 (1) 21-110
• Borwein, J. M., and R. M. Corless (2017): Gamma Function and the Factorial in the Monthly https://arxiv.org/abs/1703.05349 arXiv
• Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function American Mathematical Monthly 66 (10) 849-869
• Whitaker, E. T., and G. N. Watson (1996): A Course on Modern Analysis Cambridge University Press New York
• Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function

It provides the following functionality:

• GammaPolynomialQuotientLemma Constructor
• Retrieve the Monic Polynomial "P"
• Retrieve the Monic Polynomial "Q"
• Run the Equality Lemma over the specified a and b

Module	Computational Core Module
Library	Function Analysis Library
Project	Special Function Implementation and Analysis
Package	Special Function Property Lemma Verifiers

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
GammaPolynomialQuotientLemma(MonicPolynomial monicPolynomialP, MonicPolynomial monicPolynomialQ)	GammaPolynomialQuotientLemma Constructor

Method Summary

Modifier and Type	Method	Description
R1PropertyVerification	equalityLemma(int a, int b)	Run the Equality Lemma over the specified a and b
MonicPolynomial	monicPolynomialP()	Retrieve the Monic Polynomial "P"
MonicPolynomial	monicPolynomialQ()	Retrieve the Monic Polynomial "Q"

Methods inherited from class java.lang.Object

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

Constructor Details

GammaPolynomialQuotientLemma

public GammaPolynomialQuotientLemma(MonicPolynomial monicPolynomialP,
MonicPolynomial monicPolynomialQ)
                             throws java.lang.Exception

GammaPolynomialQuotientLemma Constructor

Parameters:

monicPolynomialP - Monic Polynomial "P"

monicPolynomialQ - Monic Polynomial "Q"

Throws:

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

Method Details

monicPolynomialP

public MonicPolynomial monicPolynomialP()

Retrieve the Monic Polynomial "P"

Returns:

The Monic Polynomial "P"

monicPolynomialQ

public MonicPolynomial monicPolynomialQ()

Retrieve the Monic Polynomial "Q"

Returns:

The Monic Polynomial "Q"

equalityLemma

public R1PropertyVerification equalityLemma(int a,
int b)

Run the Equality Lemma over the specified a and b

Parameters:

a - a

b - b

Returns:

Result of the Equality Lemma Run