Package org.drip.function.enerf

Class GeneralizedErrorFunction

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.R1ToR1Estimator

org.drip.function.enerf.GeneralizedErrorFunction

public abstract class GeneralizedErrorFunction
extends R1ToR1Estimator

GeneralizedErrorFunction implements the Generalized E_n Error Function (erf). The References are:

• Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
• Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error Function IEEE Transactions on Communications 59 (11) 2939-2944
• Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function Routines and Test Drivers ACM Transactions on Mathematical Software 19 (1) 22-32
• Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of Linear and Non-linear Heat Transfer and Diffusion https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/
• Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_function

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = R^d To R^d Function Analysis
• Package = E_n erf Series and Generators

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
int	degree()	Retrieve the Degree of the En erf
static GeneralizedErrorFunction	MacLaurin(int degree, int termCount)	Construct the Euler-MacLaurin Instance of the En erf
R1Estimate	seriesEstimateNative(double x)	Compute the Built-in Higher Order Series Estimates

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

boundedEstimate, seriesEstimate

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

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

Methods inherited from class java.lang.Object

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

Method Details

MacLaurin

public static final GeneralizedErrorFunction MacLaurin(int degree,
int termCount)

Construct the Euler-MacLaurin Instance of the E_n erf

Parameters:

degree - Degree Generalized E_n Degree

termCount - The Count of Approximation Terms

Returns:

The Euler-MacLaurin Instance of the E_n erf

degree

public int degree()

Retrieve the Degree of the E_n erf

Returns:

Degree of the E_n erf

seriesEstimateNative

public R1Estimate seriesEstimateNative(double x)

Description copied from class: R1ToR1Estimator

Compute the Built-in Higher Order Series Estimates

Overrides:

seriesEstimateNative in class R1ToR1Estimator

Parameters:

x - X

Returns:

The Built-in Higher Order Series Estimates