Package org.drip.specialfunction.derived

Class LogBigPi

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.specialfunction.derived.LogBigPi
public class LogBigPi
extends R1ToR1
LogBigPi implements the Log Gaussian Big Pi from the Log Gamma Function. 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:
  • Generate the Weierstrass Infinite Sum Series Version of Log Big Pi Estimator
  • Compute the Volume of the N-Ellipsoid
  • LogBigPi Constructor
  • Retrieve the Log Gamma Estimator

Module Product Core Module
Library Fixed Income Analytics
Project Special Function Implementation and Analysis
Package Special Functions Derived using Others
Author:
Lakshmi Krishnamurthy

  • Constructor Details

    • LogBigPi

      public LogBigPi​(R1ToR1 logGammaEstimator) throws java.lang.Exception
      LogBigPi Constructor
      Parameters:
      logGammaEstimator - The Log Gamma Estimator
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • Weierstrass

      public static final LogBigPi Weierstrass​(int termCount)
      Generate the Weierstrass Infinite Sum Series Version of Log Big Pi Estimator
      Parameters:
      termCount - Number of Terms in the Estimation
      Returns:
      The Weierstrass Infinite Sum Series Version of Log Big Pi Estimator

    • NEllipsoidVolume

      public static final double NEllipsoidVolume​(int termCount, double[] radiusArray) throws java.lang.Exception
      Compute the Volume of the N-Ellipsoid
      Parameters:
      termCount - Number of Terms in the Estimation
      radiusArray - The Array of the Ellipsoid Radii
      Returns:
      The Volume of the N-Ellipsoid
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • logGammaEstimator

      public R1ToR1 logGammaEstimator()
      Retrieve the Log Gamma Estimator
      Returns:
      The Log Gamma Estimator

    • evaluate

      public double evaluate​(double z) throws java.lang.Exception
      Description copied from class: R1ToR1
      Evaluate for the given variate
      Specified by:
      evaluate in class R1ToR1
      Parameters:
      z - Variate
      Returns:
      Returns the calculated value
      Throws:
      java.lang.Exception - Thrown if evaluation cannot be done