Package org.drip.specialfunction.digamma

Class CumulativeSeries

java.lang.Object
org.drip.specialfunction.digamma.CumulativeSeries
public class CumulativeSeries
extends java.lang.Object
CumulativeSeries implements 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 R1 To R1 Infinite Abramowitz-Stegun (2007) Cumulative Series
  • Construct the R1 To R1 Infinite Saddle Point Cumulative Series
  • Construct the R1 To R1 Gauss Cumulative Series
  • Construct the R1 To R1 Asymptotic Cumulative Series
  • Construct the R1 To R1 Exponential Asymptotic Cumulative Series
  • Construct the R1 To R1 Exponential Half-Shifted Asymptotic Cumulative Series
  • Construct the R1 To R1 Taylor Riemann-Zeta Cumulative Series

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

    • CumulativeSeries

      public CumulativeSeries()

  • Method Details

    • AbramowitzStegun2007

      public static final R1ToR1Series AbramowitzStegun2007​(int termCount)
      Construct the R1 To R1 Infinite Abramowitz-Stegun (2007) Cumulative Series
      Parameters:
      termCount - Count of the Number of Terms
      Returns:
      The R1 To R1 Infinite Abramowitz-Stegun (2007) Cumulative Series

    • MezoHoffman2017

      public static final R1ToR1Series MezoHoffman2017​(R1ToR1 saddlePointFunction, int saddlePointCount)
      Construct the R1 To R1 Infinite Saddle Point Cumulative Series
      Parameters:
      saddlePointFunction - The Saddle Point Generation Function
      saddlePointCount - The Saddle Point Count
      Returns:
      The R1 To R1 Infinite Saddle Point Cumulative Series

    • Gauss

      public static final R1ToR1Series Gauss​(int termCount)
      Construct the R1 To R1 Gauss Cumulative Series
      Parameters:
      termCount - Count of the Number of Terms
      Returns:
      The R1 To R1 Gauss Cumulative Series

    • Asymptotic

      public static final R1ToR1Series Asymptotic()
      Construct the R1 To R1 Asymptotic Cumulative Series
      Returns:
      The R1 To R1 Asymptotic Cumulative Series

    • ExponentialAsymptote

      public static final R1ToR1Series ExponentialAsymptote()
      Construct the R1 To R1 Exponential Asymptotic Cumulative Series
      Returns:
      The R1 To R1 Exponential Asymptotic Cumulative Series

    • ExponentialAsymptoteHalfShifted

      public static final R1ToR1Series ExponentialAsymptoteHalfShifted()
      Construct the R1 To R1 Exponential Half-Shifted Asymptotic Cumulative Series
      Returns:
      The R1 To R1 Exponential Half-Shifted Asymptotic Cumulative Series

    • TaylorRiemannZeta

      public static final R1ToR1Series TaylorRiemannZeta​(R1ToR1 riemannZetaEstimator, int termCount)
      Construct the R1 To R1 Taylor Riemann-Zeta Cumulative Series
      Parameters:
      riemannZetaEstimator - The Riemann-Zeta Estimator
      termCount - Count of the Number of Terms
      Returns:
      The R1 To R1 Taylor Riemann-Zeta Cumulative Series