Package org.drip.specialfunction.gamma

Class EulerIntegralSecondKind

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.specialfunction.gamma.EulerIntegralSecondKind
public class EulerIntegralSecondKind
extends R1ToR1
EulerIntegralSecondKind implements the Euler's Second Kind Integral Version of the 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:
  • EulerIntegralSecondKind Constructor

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

  • Constructor Details

    • EulerIntegralSecondKind

      public EulerIntegralSecondKind​(DerivativeControl derivativeControl)
      EulerIntegralSecondKind Constructor
      Parameters:
      derivativeControl - The Derivative Control

  • Method Details

    • evaluate

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

    • derivative

      public double derivative​(double z, int order) throws java.lang.Exception
      Description copied from class: R1ToR1
      Calculate the derivative as a double
      Overrides:
      derivative in class R1ToR1
      Parameters:
      z - Variate at which the derivative is to be calculated
      order - Order of the derivative to be computed
      Returns:
      The Derivative
      Throws:
      java.lang.Exception - Thrown if Inputs are Invalid

    • poleResidue

      public PoleResidue poleResidue​(double x)
      Description copied from class: R1ToR1
      Compute the Residue if the Variate is a Pole
      Overrides:
      poleResidue in class R1ToR1
      Parameters:
      x - Variate
      Returns:
      The Residue if the Variate is a Pole