Package org.drip.specialfunction.property

Class BetaEqualityLemma

java.lang.Object

org.drip.specialfunction.property.BetaEqualityLemma

public class BetaEqualityLemma
extends java.lang.Object

BetaEqualityLemma implements the Equality Lemmas for the Beta Estimation. The References are:

• Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
• 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): Beta Function https://en.wikipedia.org/wiki/Beta_function
• Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function

It provides the following functionality:

• Construct the Beta Equality Lemma Identity #1
• Construct the Beta Equality Lemma Identity #2
• Construct the Beta Equality Lemma Identity #3
• Construct the Beta Equality Lemma Identity #4
• Construct the Beta Equality Lemma Identity #5
• Construct the Beta Equality Lemma Identity #6

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
BetaEqualityLemma()

Method Summary

Modifier and Type	Method	Description
static R2ToR1Property	Identity1()	Construct the Identity #1 Verifier
static R2ToR1Property	Identity2()	Construct the Identity #2 Verifier
static R2ToR1Property	Identity3()	Construct the Identity #3 Verifier
static R2ToR1Property	Identity4()	Construct the Identity #4 Verifier
static R1ToR1Property	Identity5()	Construct the Identity #5 Verifier
static R1ToR1Property	Identity6()	Construct the Identity #6 Verifier

Methods inherited from class java.lang.Object

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

Constructor Details

BetaEqualityLemma

public BetaEqualityLemma()

Method Details

Identity1

public static final R2ToR1Property Identity1()

Construct the Identity #1 Verifier

Returns:

The Identity #1 Verifier

Identity2

public static final R2ToR1Property Identity2()

Construct the Identity #2 Verifier

Returns:

The Identity #2 Verifier

Identity3

public static final R2ToR1Property Identity3()

Construct the Identity #3 Verifier

Returns:

The Identity #3 Verifier

Identity4

public static final R2ToR1Property Identity4()

Construct the Identity #4 Verifier

Returns:

The Identity #4 Verifier

Identity5

public static final R1ToR1Property Identity5()

Construct the Identity #5 Verifier

Returns:

The Identity #5 Verifier

Identity6

public static final R1ToR1Property Identity6()

Construct the Identity #6 Verifier

Returns:

The Identity #6 Verifier