Package org.drip.specialfunction.property

Class DigammaSaddlePointEqualityLemma

java.lang.Object
org.drip.specialfunction.property.DigammaSaddlePointEqualityLemma
public class DigammaSaddlePointEqualityLemma
extends java.lang.Object
DigammaSaddlePointEqualityLemma contains the Verifiable Equality Lemmas for the Digamma Saddle Points. 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 Quadratic Reciprocal Sum Verifier
  • Construct the Cubic Reciprocal Sum Verifier
  • Construct the Quartic Reciprocal Sum Verifier
  • Construct the First Quadratic Polynomial Reciprocal Sum Verifier
  • Construct the Second Quadratic Polynomial Reciprocal Sum 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

    • DigammaSaddlePointEqualityLemma

      public DigammaSaddlePointEqualityLemma()

  • Method Details

    • QuadraticReciprocalSum

      public static final R1ToR1Property QuadraticReciprocalSum​(R1ToR1 digammaSaddlePointsFunction)
      Construct the Quadratic Reciprocal Sum Verifier
      Parameters:
      digammaSaddlePointsFunction - Digamma Saddle Points Function
      Returns:
      The Quadratic Reciprocal Sum Verifier

    • CubicReciprocalSum

      public static final R1ToR1Property CubicReciprocalSum​(R1ToR1 digammaSaddlePointsFunction)
      Construct the Cubic Reciprocal Sum Verifier
      Parameters:
      digammaSaddlePointsFunction - Digamma Saddle Points Function
      Returns:
      The Cubic Reciprocal Sum Verifier

    • QuarticReciprocalSum

      public static final R1ToR1Property QuarticReciprocalSum​(R1ToR1 digammaSaddlePointsFunction)
      Construct the Quartic Reciprocal Sum Verifier
      Parameters:
      digammaSaddlePointsFunction - Digamma Saddle Points Function
      Returns:
      The Quartic Reciprocal Sum Verifier

    • QuadraticPolynomialReciprocalSum1

      public static final R1ToR1Property QuadraticPolynomialReciprocalSum1​(R1ToR1 digammaSaddlePointsFunction)
      Construct the First Quadratic Polynomial Reciprocal Sum Verifier
      Parameters:
      digammaSaddlePointsFunction - Digamma Saddle Points Function
      Returns:
      The First Quadratic Polynomial Reciprocal Sum Verifier

    • QuadraticPolynomialReciprocalSum2

      public static final R1ToR1Property QuadraticPolynomialReciprocalSum2​(R1ToR1 digammaSaddlePointsFunction)
      Construct the Second Quadratic Polynomial Reciprocal Sum Verifier
      Parameters:
      digammaSaddlePointsFunction - Digamma Saddle Points Function
      Returns:
      The Second Quadratic Polynomial Reciprocal Sum Verifier