Package org.drip.function.e2erf

Class MacLaurinSeries

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.numerical.estimation.RxToR1Series

org.drip.numerical.estimation.R1ToR1Series

org.drip.function.e2erf.MacLaurinSeries

public class MacLaurinSeries
extends R1ToR1Series

MacLaurinSeries implements the E₂ MacLaurin Series Term. 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 = E₂ erf and erf^-1 Implementations

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
MacLaurinSeries(MacLaurinSeriesTerm macLaurinSeriesTerm, java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap)	MacLaurinSeries Constructor

Method Summary

Modifier and Type	Method	Description
static MacLaurinSeries	ERF(int termCount)	Construct the E2 erf MacLaurin Series Generator Version
static MacLaurinSeries	ERFI(int termCount)	Construct the E2 erfi MacLaurin Series Generator Version
static double	ERFICoefficient(int seriesIndex)	Generate the ERFI E2 MacLaurin Coefficient corresponding to the specified Series Index

Methods inherited from class org.drip.numerical.estimation.R1ToR1Series

cumulative, derivative, evaluate, generate, r1ToR1SeriesTerm

Methods inherited from class org.drip.numerical.estimation.RxToR1Series

proportional, termWeightMap

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

antiDerivative, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

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

Constructor Details

MacLaurinSeries

public MacLaurinSeries(MacLaurinSeriesTerm macLaurinSeriesTerm,
java.util.TreeMap<java.lang.Integer,java.lang.Double> termWeightMap)
                throws java.lang.Exception

MacLaurinSeries Constructor

Parameters:

macLaurinSeriesTerm - E₂ erf MacLaurin Series Term

termWeightMap - Series Term Weight Map

Throws:

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

Method Details

ERFICoefficient

public static final double ERFICoefficient(int seriesIndex)

Generate the ERFI E₂ MacLaurin Coefficient corresponding to the specified Series Index

Parameters:

seriesIndex - Series Index

Returns:

The ERFI E₂ MacLaurin Coefficient corresponding to the specified Series Index

ERF

public static final MacLaurinSeries ERF(int termCount)

Construct the E₂ erf MacLaurin Series Generator Version

Parameters:

termCount - Count of the Number of Terms

Returns:

E₂ erf MacLaurin Series Generator Version

ERFI

public static final MacLaurinSeries ERFI(int termCount)

Construct the E₂ erfi MacLaurin Series Generator Version

Parameters:

termCount - Count of the Number of Terms

Returns:

The E₂ erfi MacLaurin Series Generator Version