Package org.drip.specialfunction.loggamma

Class InfiniteSumSeries

java.lang.Object
org.drip.specialfunction.loggamma.InfiniteSumSeries
public class InfiniteSumSeries
extends java.lang.Object
InfiniteSumSeries implements Infinite Sum 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 R1 To R1 Infinite Euler Sum Series
  • Construct the R1 To R1 Infinite Weierstrass Sum Series
  • Construct the R1 To R1 Malmsten-Blagouchine Fourier Series
  • Construct the R1 To R1 Blagouchine (2015) Series

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
    InfiniteSumSeries()  

  • Method Summary

    Modifier and Type Method Description
    static R1ToR1Series Blagouchine2015​(int termCount)
    Construct the R1 To R1 Blagouchine (2015) Series
    static R1ToR1Series Euler​(int termCount)
    Construct the R1 To R1 Infinite Euler Sum Series
    static R1ToR1Series Fourier​(int termCount)
    Construct the R1 To R1 Malmsten-Blagouchine Fourier Series
    static R1ToR1Series Weierstrass​(int termCount)
    Construct the R1 To R1 Infinite Weierstrass Sum Series

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • InfiniteSumSeries

      public InfiniteSumSeries()

  • Method Details

    • Euler

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

    • Weierstrass

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

    • Fourier

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

    • Blagouchine2015

      public static final R1ToR1Series Blagouchine2015​(int termCount)
      Construct the R1 To R1 Blagouchine (2015) Series
      Parameters:
      termCount - Count of the Number of Terms
      Returns:
      The R1 To R1 Blagouchine (2015) Series