Package org.drip.specialfunction.property

Class BigPiEqualityLemma

java.lang.Object
org.drip.specialfunction.property.BigPiEqualityLemma
public class BigPiEqualityLemma
extends java.lang.Object
BigPiEqualityLemma verifies the Specified Property Lemmas of the Big Pi Function. 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:
  • Construct the Reflection Formula Verifier
  • Construct the Multiplication Formula Verifier

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
    BigPiEqualityLemma()  

  • Method Summary

    Modifier and Type Method Description
    static R1ToR1Property MultiplicationFormula​(int m)
    Construct the Multiplication Formula Verifier
    static R1ToR1Property ReflectionFormula()
    Construct the Reflection Formula Verifier

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • BigPiEqualityLemma

      public BigPiEqualityLemma()

  • Method Details

    • ReflectionFormula

      public static final R1ToR1Property ReflectionFormula()
      Construct the Reflection Formula Verifier
      Returns:
      The Reflection Formula Verifier

    • MultiplicationFormula

      public static final R1ToR1Property MultiplicationFormula​(int m)
      Construct the Multiplication Formula Verifier
      Parameters:
      m - m
      Returns:
      The Multiplication Formula Verifier