Package org.drip.numerical.estimation

Class R1ToR1IntegrandLimitEstimator

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.R1ToR1Estimator

org.drip.numerical.estimation.R1ToR1IntegrandLimitEstimator

Direct Known Subclasses:

ErrorFunction, ErrorFunctionComplement

public abstract class R1ToR1IntegrandLimitEstimator
extends R1ToR1Estimator

R1ToR1IntegrandLimitEstimator exposes the Stubs behind the Integrand Based R¹ - R¹ Approximate Numerical Estimators with the Limits as the Variate. The References are:

• Mortici, C. (2011): Improved Asymptotic Formulas for the Gamma Function Computers and Mathematics with Applications 61 (11) 3364-3369
• National Institute of Standards and Technology (2018): NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/5.11
• Nemes, G. (2010): On the Coefficients of the Asymptotic Expansion of n! https://arxiv.org/abs/1003.2907 arXiv
• Toth V. T. (2016): Programmable Calculators – The Gamma Function http://www.rskey.org/CMS/index.php/the-library/11
• Wikipedia (2019): Stirling's Approximation https://en.wikipedia.org/wiki/Stirling%27s_approximation

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Function Numerical Estimates/Corrections/Bounds

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
double	evaluate(double x)	Evaluate for the given variate
abstract R1ToR1	integrand()	Retrieve the R1 To R1 erf Integrand
double	leftLimit()	Retrieve the Left Limit

Methods inherited from class org.drip.numerical.estimation.R1ToR1Estimator

boundedEstimate, seriesEstimate, seriesEstimateNative

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

antiDerivative, 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

integrand

public abstract R1ToR1 integrand()

Retrieve the R¹ To R¹ erf Integrand

Returns:

The R¹ To R¹ erf Integrand

leftLimit

public double leftLimit()

Retrieve the Left Limit

Returns:

The Left Limit

evaluate

public double evaluate(double x)
                throws java.lang.Exception

Description copied from class: R1ToR1

Evaluate for the given variate

Specified by:

evaluate in class R1ToR1

Parameters:

x - Variate

Returns:

Returns the calculated value

Throws:

java.lang.Exception - Thrown if evaluation cannot be done