Package org.drip.specialfunction.digamma

Class CumulativeSeriesTerm

java.lang.Object
org.drip.specialfunction.digamma.CumulativeSeriesTerm
public class CumulativeSeriesTerm
extends java.lang.Object
CumulativeSeriesTerm implements a Single Term in the Cumulative Series for Digamma Estimation. 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:
  • Construct the Abramowitz-Stegun (2017) Cumulative Sum Series Term for DiGamma
  • Construct the Mezo-Hoffman (2017) Cumulative Sum Series Term for DiGamma
  • Construct the Gauss Cumulative Sum Series Term for DiGamma
  • Construct the Asymptotic Cumulative Sum Series Term for DiGamma
  • Construct the Asymptotic Cumulative Sum Series Term for exp (-diGamma)
  • Construct the Asymptotic Cumulative Sum Series Term for exp (diGamma + 0.5)
  • Construct the Taylor-Riemann Zeta Series Term for Digamma
  • Construct the Newton-Stern Series Term for Digamma

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

  • Constructor Details

    • CumulativeSeriesTerm

      public CumulativeSeriesTerm()

  • Method Details

    • AbramowitzStegun2007

      public static final R1ToR1SeriesTerm AbramowitzStegun2007()
      Construct the Abramowitz-Stegun (2007) Cumulative Sum Series Term for DiGamma
      Returns:
      The Abramowitz-Stegun (2007) Cumulative Sum Series Term for DiGamma

    • MezoHoffman2017

      public static final R1ToR1SeriesTerm MezoHoffman2017​(double[] saddlePointArray)
      Construct the Mezo-Hoffman (2017) Cumulative Sum Series Term for DiGamma
      Parameters:
      saddlePointArray - Array of the Saddle Points
      Returns:
      The Mezo-Hoffman (2017) Cumulative Sum Series Term for DiGamma

    • Gauss

      public static final R1ToR1SeriesTerm Gauss​(int termCount)
      Construct the Gauss Cumulative Sum Series Term for DiGamma
      Parameters:
      termCount - Term Count
      Returns:
      The Gauss Cumulative Sum Series Term for DiGamma

    • Asymptotic

      public static final R1ToR1SeriesTerm Asymptotic()
      Construct the Asymptotic Cumulative Sum Series Term for DiGamma
      Returns:
      The Asymptotic Cumulative Sum Series Term for DiGamma

    • ExponentialAsymptote

      public static final R1ToR1SeriesTerm ExponentialAsymptote()
      Construct the Asymptotic Cumulative Sum Series Term for exp (-diGamma)
      Returns:
      The Asymptotic Cumulative Sum Series Term for exp (-diGamma)

    • ExponentialAsymptoteHalfShifted

      public static final R1ToR1SeriesTerm ExponentialAsymptoteHalfShifted()
      Construct the Asymptotic Cumulative Sum Series Term for exp (diGamma + 0.5)
      Returns:
      The Asymptotic Cumulative Sum Series Term for exp (-diGamma + 0.5)

    • TaylorRiemannZeta

      public static final R1ToR1SeriesTerm TaylorRiemannZeta​(R1ToR1 riemannZetaEstimator)
      Construct the Taylor-Riemann Zeta Series Term for Digamma
      Parameters:
      riemannZetaEstimator - The Riemann-Zeta Estimator
      Returns:
      The Taylor-Riemann Zeta Series Term for Digamma

    • NewtonStern

      public static final R1ToR1SeriesTerm NewtonStern()
      Construct the Newton-Stern Series Term for Digamma
      Returns:
      The Newton-Stern Series Term for Digamma