Package org.drip.specialfunction.digamma

Class SaddlePoints

java.lang.Object
org.drip.specialfunction.digamma.SaddlePoints
public class SaddlePoints
extends java.lang.Object
SaddlePoints contains the Hermite Based Saddle Point Roots of the Digamma Function. The References are:

  • Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
  • Blagouchine, I. V. (2018): Three Notes on Ser's and Hasse's Representations for the Zeta-Functions https://arxiv.org/abs/1606.02044 arXiv
  • Mezo, I., and M. E. Hoffman (2017): Zeros of the Digamma Function and its Barnes G-function Analogue Integral Transforms and Special Functions 28 (28) 846-858
  • Whitaker, E. T., and G. N. Watson (1996): A Course on Modern Analysis Cambridge University Press New York
  • Wikipedia (2019): Digamma Function https://en.wikipedia.org/wiki/Digamma_function
It provides the following functionality:
  • Generate the Set of Leading Digamma Saddle Points
  • Construct the R1 to R1 Hermite Digamma Root Function
  • Construct the R1 to R1 Hermite Extension Digamma Root Function
  • Construct the R1 to R1 Hermite Enhancement Digamma Root Function
  • Construct the R1 to R1 Mezo-Hoffman (2017) Digamma Root Function
  • Generate the Array of Leading Roots

Module Product Core Module
Library Fixed Income Analytics
Project Special Function Implementation and Analysis
Package Estimation Techniques for Digamma Function
Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    SaddlePoints()  

  • Method Summary

    Modifier and Type Method Description
    static R1ToR1 Hermite()
    Construct the R1 to R1 Hermite Digamma Root Function
    static R1ToR1 HermiteEnhancement()
    Construct the R1 to R1 Hermite Enhancement Digamma Root Function
    static R1ToR1 HermiteExtension()
    Construct the R1 to R1 Hermite Extension Digamma Root Function
    static double[] LeadingRoots​(R1ToR1 rootFunction, int rootCount)
    Generate the Array of Leading Roots
    static java.util.TreeSet<java.lang.Double> LeadingZeros()
    Generate the Set of Leading Digamma Saddle Points
    static R1ToR1 MezoHoffman2017()
    Construct the R1 to R1 Mezo-Hoffman (2017) Digamma Root Function

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • SaddlePoints

      public SaddlePoints()

  • Method Details

    • LeadingZeros

      public static final java.util.TreeSet<java.lang.Double> LeadingZeros()
      Generate the Set of Leading Digamma Saddle Points
      Returns:
      Set of Leading Digamma Saddle Points

    • Hermite

      public static final R1ToR1 Hermite()
      Construct the R1 to R1 Hermite Digamma Root Function
      Returns:
      The R1 to R1 Hermite Digamma Root Function

    • HermiteExtension

      public static final R1ToR1 HermiteExtension()
      Construct the R1 to R1 Hermite Extension Digamma Root Function
      Returns:
      The R1 to R1 Hermite Extension Digamma Root Function

    • HermiteEnhancement

      public static final R1ToR1 HermiteEnhancement()
      Construct the R1 to R1 Hermite Enhancement Digamma Root Function
      Returns:
      The R1 to R1 Hermite Enhancement Digamma Root Function

    • MezoHoffman2017

      public static final R1ToR1 MezoHoffman2017()
      Construct the R1 to R1 Mezo-Hoffman (2017) Digamma Root Function
      Returns:
      The R1 to R1 Mezo-Hoffman (2017) Digamma Root Function

    • LeadingRoots

      public static final double[] LeadingRoots​(R1ToR1 rootFunction, int rootCount)
      Generate the Array of Leading Roots
      Parameters:
      rootFunction - The Root Generation Function
      rootCount - The Root Count
      Returns:
      The Array of Leading Roots