Package org.drip.specialfunction.property

Class DigammaInequalityLemma

java.lang.Object
org.drip.specialfunction.property.DigammaInequalityLemma
public class DigammaInequalityLemma
extends java.lang.Object
DigammaInequalityLemma contains the Verifiable Inequality Lemmas for the Digamma 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:
  • Generate the Digamma Asymptotic Left Inequality Verifier
  • Generate the Digamma Asymptotic Right Inequality Verifier
  • Generate the Digamma (0, 1) Left Bound Inequality Verifier
  • Generate the Digamma (0, 1) Right Bound Verifier
  • Generate the Bernstein-Binet Left Bound Inequality Verifier
  • Generate the Bernstein-Binet Right Bound Inequality Verifier
  • Generate the Elezovic-Giordano-Pecaric Left Bound Inequality Verifier
  • Generate the Elezovic-Giordano-Pecaric Right Bound Inequality Verifier
  • Generate the Alzer (1997) Digamma Difference Lemma Verifier
  • Generate the Alzer-Jameson (2017) Inequality 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 Details

    • DigammaInequalityLemma

      public DigammaInequalityLemma()

  • Method Details

    • LeftAsymptote

      public static final R1ToR1Property LeftAsymptote()
      Generate the Digamma Asymptotic Left Inequality Verifier
      Returns:
      The Digamma Asymptotic Left Inequality Verifier

    • RightAsymptote

      public static final R1ToR1Property RightAsymptote()
      Generate the Digamma Asymptotic Right Inequality Verifier
      Returns:
      The Digamma Asymptotic Right Inequality Verifier

    • ZeroOneLeftBound

      public static final R1ToR1Property ZeroOneLeftBound()
      Generate the Digamma (0, 1) Left Bound Inequality Verifier
      Returns:
      The Digamma (0, 1) Left Bound Inequality Verifier

    • ZeroOneRightBound

      public static final R1ToR1Property ZeroOneRightBound()
      Generate the Digamma (0, 1) Right Bound Verifier
      Returns:
      The Digamma (0, 1) Right Bound Verifier

    • BernsteinBinetLeftBound

      public static final R1ToR1Property BernsteinBinetLeftBound()
      Generate the Bernstein-Binet Left Bound Inequality Verifier
      Returns:
      The Bernstein-Binet Left Bound Inequality Verifier

    • BernsteinBinetRightBound

      public static final R1ToR1Property BernsteinBinetRightBound()
      Generate the Bernstein-Binet Right Bound Inequality Verifier
      Returns:
      The Bernstein-Binet Right Bound Inequality Verifier

    • ElezovicGiordanoPecaricLeftBound

      public static final R1ToR1Property ElezovicGiordanoPecaricLeftBound()
      Generate the Elezovic-Giordano-Pecaric Left Bound Inequality Verifier
      Returns:
      The Elezovic-Giordano-Pecaric Left Bound Inequality Verifier

    • ElezovicGiordanoPecaricRightBound

      public static final R1ToR1Property ElezovicGiordanoPecaricRightBound()
      Generate the Elezovic-Giordano-Pecaric Right Bound Inequality Verifier
      Returns:
      The Elezovic-Giordano-Pecaric Right Bound Inequality Verifier

    • AlzerDifference1997

      public static final R1ToR1Property AlzerDifference1997​(double s)
      Generate the Alzer (1997) Digamma Difference Lemma Verifier
      Parameters:
      s - s
      Returns:
      The Alzer (1997) Digamma Difference Lemma Verifier

    • AlzerJameson2017

      public static final R1ToR1Property AlzerJameson2017()
      Generate the Alzer-Jameson (2017) Inequality Verifier
      Returns:
      The Alzer-Jameson (2017) Inequality Verifier