Package org.drip.specialfunction.property

Class DigammaEqualityLemma

java.lang.Object
org.drip.specialfunction.property.DigammaEqualityLemma
public class DigammaEqualityLemma
extends java.lang.Object
DigammaEqualityLemma contains the Verifiable Equality Lemmas of 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 (0, 1) Reflection Formula Verifier
  • Generate the Blagouchine Finite Summation Identity Verifier #1
  • Generate the Blagouchine Finite Summation Identity Verifier #2
  • Generate the Blagouchine Finite Summation Identity Verifier #3
  • Generate the Blagouchine Finite Summation Identity Verifier #4
  • Generate the Blagouchine Finite Summation Identity Verifier #5
  • Generate the Blagouchine Finite Summation Identity Verifier #6
  • Generate the Blagouchine Finite Summation Identity Verifier #7
  • Generate the Blagouchine Finite Summation Identity Verifier #8
  • Generate the Blagouchine Finite Summation Identity Verifier #9
  • Generate the Blagouchine Finite Summation Identity Verifier #10

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

    • DigammaEqualityLemma

      public DigammaEqualityLemma()

  • Method Details

    • ReflectionFormula

      public static final R1ToR1Property ReflectionFormula()
      Generate the Digamma (0, 1) Reflection Formula Verifier
      Returns:
      The Digamma (0, 1) Reflection Formula Verifier

    • SummationIdentity1

      public static final R1ToR1Property SummationIdentity1()
      Generate the Gaussian Finite Summation Identity Verifier #1
      Returns:
      The Gaussian Finite Summation Identity Verifier #1

    • SummationIdentity2

      public static final R1ToR1Property SummationIdentity2​(int k)
      Generate the Gaussian Finite Summation Identity Verifier #2
      Parameters:
      k - k
      Returns:
      The Gaussian Finite Summation Identity Verifier #2

    • SummationIdentity3

      public static final R1ToR1Property SummationIdentity3​(int k)
      Generate the Gaussian Finite Summation Identity Verifier #3
      Parameters:
      k - k
      Returns:
      The Gaussian Finite Summation Identity Verifier #3

    • SummationIdentity4

      public static final R1ToR1Property SummationIdentity4​(int k)
      Generate the Blagouchine Finite Summation Identity Verifier #4
      Parameters:
      k - k
      Returns:
      The Blagouchine Finite Summation Identity Verifier #4

    • SummationIdentity5

      public static final R1ToR1Property SummationIdentity5​(int k)
      Generate the Blagouchine Finite Summation Identity Verifier #5
      Parameters:
      k - k
      Returns:
      The Blagouchine Finite Summation Identity Verifier #5

    • SummationIdentity6

      public static final R1ToR1Property SummationIdentity6()
      Generate the Blagouchine Finite Summation Identity Verifier #6
      Returns:
      The Blagouchine Finite Summation Identity Verifier #6

    • SummationIdentity7

      public static final R1ToR1Property SummationIdentity7()
      Generate the Blagouchine Finite Summation Identity Verifier #7
      Returns:
      The Blagouchine Finite Summation Identity Verifier #7

    • SummationIdentity8

      public static final R1ToR1Property SummationIdentity8​(double l)
      Generate the Blagouchine Finite Summation Identity Verifier #8
      Parameters:
      l - l
      Returns:
      The Blagouchine Finite Summation Identity Verifier #8

    • SummationIdentity9

      public static final R1ToR1Property SummationIdentity9​(double l)
      Generate the Blagouchine Finite Summation Identity Verifier #9
      Parameters:
      l - l
      Returns:
      The Blagouchine Finite Summation Identity Verifier #9

    • SummationIdentity10

      public static final R1ToR1Property SummationIdentity10()
      Generate the Blagouchine Finite Summation Identity Verifier #10
      Returns:
      The Blagouchine Finite Summation Identity Verifier #10