Package org.drip.specialfunction.loggamma

Class InfiniteSumSeriesTerm

java.lang.Object
org.drip.specialfunction.loggamma.InfiniteSumSeriesTerm
public class InfiniteSumSeriesTerm
extends java.lang.Object
InfiniteSumSeriesTerm implements a Single Term in the Infinite Series for Log Gamma Estimation. 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 Euler Infinite Sum Series Term for Log Gamma
  • Construct the Weierstrass Infinite Sum Series Term for Log Gamma
  • Construct the Malmsten-Blagouchine Fourier Series Term for Log Gamma
  • Construct the Blagouchine (2015) Series Term for Log Gamma

Module Computational Core Module
Library Function Analysis Library
Project Special Function Implementation and Analysis
Package Analytic/Series/Integral Log Gamma Estimators
Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    InfiniteSumSeriesTerm()  

  • Method Summary

    Modifier and Type Method Description
    static R1ToR1SeriesTerm Blagouchine2015()
    Construct the Blagouchine (2015) Series Term for Log Gamma
    static R1ToR1SeriesTerm Euler()
    Construct the Euler Infinite Sum Series Term for Log Gamma
    static R1ToR1SeriesTerm Fourier()
    Construct the Malmsten-Blagouchine Fourier Series Term for Log Gamma
    static R1ToR1SeriesTerm Weierstrass()
    Construct the Weierstrass Infinite Sum Series Term for Log Gamma

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • InfiniteSumSeriesTerm

      public InfiniteSumSeriesTerm()

  • Method Details

    • Euler

      public static final R1ToR1SeriesTerm Euler()
      Construct the Euler Infinite Sum Series Term for Log Gamma
      Returns:
      The Euler Infinite Sum Series Term for Log Gamma

    • Weierstrass

      public static final R1ToR1SeriesTerm Weierstrass()
      Construct the Weierstrass Infinite Sum Series Term for Log Gamma
      Returns:
      The Weierstrass Infinite Sum Series Term for Log Gamma

    • Fourier

      public static final R1ToR1SeriesTerm Fourier()
      Construct the Malmsten-Blagouchine Fourier Series Term for Log Gamma
      Returns:
      The Malmsten-Blagouchine Fourier Series Term for Log Gamma

    • Blagouchine2015

      public static final R1ToR1SeriesTerm Blagouchine2015()
      Construct the Blagouchine (2015) Series Term for Log Gamma
      Returns:
      The Blagouchine (2015) Series Term for Log Gamma