Package org.drip.specialfunction.scaledexponential

Class RelaxationTimeDistributionSeriesTerm

java.lang.Object
org.drip.numerical.estimation.R1ToR1SeriesTerm
org.drip.specialfunction.scaledexponential.RelaxationTimeDistributionSeriesTerm
public class RelaxationTimeDistributionSeriesTerm
extends R1ToR1SeriesTerm
RelaxationTimeDistributionSeriesTerm implements the Series Term in the Expansion of the Relaxation Time Distribution Function. The References are:

  • Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015): Tables of Integrals, Series, and Products Academic Press
  • Hilfer, J. (2002): H-function Representations for Stretched Exponential Relaxation and non-Debye Susceptibilities in Glassy Systems Physical Review E 65 (6) 061510
  • Wikipedia (2019): Stretched Exponential Function https://en.wikipedia.org/wiki/Stretched_exponential_function
  • Wuttke, J. (2012): Laplace-Fourier Transform of the Stretched Exponential Function: Analytic Error-Bounds, Double Exponential Transform, and Open Source Implementation libkw Algorithm 5 (4) 604-628
  • Zorn, R. (2002): Logarithmic Moments of Relaxation Time Distributions Journal of Chemical Physics 116 (8) 3204-3209
It provides the following functionality:
  • RelaxationTimeDistributionSeriesTerm Constructor
  • Retrieve the Beta
  • Retrieve the Gamma Estimator

Module Computational Core Module
Library Function Analysis Library
Project Special Function Implementation and Analysis
Package Scaled Exponential Function Implementation Distribution
Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    RelaxationTimeDistributionSeriesTerm​(double beta, R1ToR1 gammaEstimator)
    RelaxationTimeDistributionSeriesTerm Constructor

  • Method Summary

    Modifier and Type Method Description
    double beta()
    Retrieve the Beta
    R1ToR1 gammaEstimator()
    Retrieve the Gamma Estimator
    double value​(int order, double u)
    Compute the Value of the R1 To R1 Series Expansion Term

    Methods inherited from class org.drip.numerical.estimation.R1ToR1SeriesTerm

    Asymptotic, derivative, InvertedRisingExponential, Taylor

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • RelaxationTimeDistributionSeriesTerm

      public RelaxationTimeDistributionSeriesTerm​(double beta, R1ToR1 gammaEstimator) throws java.lang.Exception
      RelaxationTimeDistributionSeriesTerm Constructor
      Parameters:
      beta - Beta
      gammaEstimator - Gamma Estimator
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • beta

      public double beta()
      Retrieve the Beta
      Returns:
      The Beta

    • gammaEstimator

      public R1ToR1 gammaEstimator()
      Retrieve the Gamma Estimator
      Returns:
      The Gamma Estimator

    • value

      public double value​(int order, double u) throws java.lang.Exception
      Description copied from class: R1ToR1SeriesTerm
      Compute the Value of the R1 To R1 Series Expansion Term
      Specified by:
      value in class R1ToR1SeriesTerm
      Parameters:
      order - Order of the R1 To R1 Series Expansion Term
      u - X
      Returns:
      The Value of the R1 To R1 Series Expansion Term
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid