Package org.drip.specialfunction.scaledexponential

Class RelaxationTimeDistributionSeriesEstimator

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.specialfunction.definition.RelaxationTimeDistributionEstimator

org.drip.specialfunction.scaledexponential.RelaxationTimeDistributionSeriesEstimator

public class RelaxationTimeDistributionSeriesEstimator
extends RelaxationTimeDistributionEstimator

RelaxationTimeDistributionSeriesEstimator exposes the Series-based Estimator for 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:

• Construct a Standard Instance of RelaxationTimeDistributionSeriesEstimator
• Retrieve the R¹ to R¹ Relaxation Time Distribution Series

Module	Computational Core Module
Library	Function Analysis Library
Project	Special Function Implementation and Analysis
Package	Scaled Exponential Function Implementation Distribution

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
double	relaxationTimeDensity(double t)	Compute the Relaxation Time Density
R1ToR1Series	series()	Retrieve the R1 to R1 Relaxation Time Distribution Series
static RelaxationTimeDistributionSeriesEstimator	Standard(double beta, R1ToR1 gammaEstimator, int termCount)	Construct a Standard Instance of RelaxationTimeDistributionSeriesEstimator

Methods inherited from class org.drip.specialfunction.definition.RelaxationTimeDistributionEstimator

evaluate, gFunction, GFunctionHalfBeta

Methods inherited from class org.drip.function.definition.R1ToR1

antiDerivative, conditionNumber, derivative, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

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

Method Details

Standard

public static final RelaxationTimeDistributionSeriesEstimator Standard(double beta,
R1ToR1 gammaEstimator,
int termCount)

Construct a Standard Instance of RelaxationTimeDistributionSeriesEstimator

Parameters:

beta - The beta

gammaEstimator - The Gamma Estimator

termCount - Count of the Number of Terms

Returns:

Standard Instance of RelaxationTimeDistributionSeriesEstimator

series

public R1ToR1Series series()

Retrieve the R¹ to R¹ Relaxation Time Distribution Series

Returns:

The R¹ to R¹ Relaxation Time Distribution Series

relaxationTimeDensity

public double relaxationTimeDensity(double t)
                             throws java.lang.Exception

Description copied from class: RelaxationTimeDistributionEstimator

Compute the Relaxation Time Density

Specified by:

relaxationTimeDensity in class RelaxationTimeDistributionEstimator

Parameters:

t - Time Instant

Returns:

The Relaxation Time Density

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid