Package org.drip.specialfunction.ode

Class SecondOrder

java.lang.Object

org.drip.specialfunction.ode.SecondOrder

Direct Known Subclasses:

HilleQForm2F1, SecondOrderBessel, SecondOrderHelmholtz, SecondOrderModifiedBessel, SecondOrderRiccatiBessel

public class SecondOrder
extends java.lang.Object

SecondOrder exposes the Coefficient Terms in the Second-Order ODE. The References are:

• Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series SIAM Journal on Mathematical Analysis 13 (2) 295-308
• Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation Journal of Symbolic Computation 20 (4) 399-417
• Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the Sum of a (_2^3)F(a,b;c;z) Journal of Computational and Applied Mathematics 72 293-300
• National Institute of Standards and Technology (2019): Hyper-geometric Function https://dlmf.nist.gov/15
• Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_function

It provides the following functionality:

• SecondOrder Constructor
• Retrieve the R² to R¹ Second Derivative Coefficient Function
• Retrieve the R² to R¹ First Derivative Coefficient Function
• Retrieve the R² to R¹ Zero Derivative Coefficient Function
• Retrieve the Ordered Regular Singular Points of the Second Order ODE

Module	Computational Core Module
Library	Function Analysis Library
Project	Special Function Implementation and Analysis
Package	Special Function Ordinary Differential Equations

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
SecondOrder(R2ToR1 secondDerivativeCoefficient, R2ToR1 firstDerivativeCoefficient, R2ToR1 zeroDerivativeCoefficient)	SecondOrder Constructor

Method Summary

Modifier and Type	Method	Description
R2ToR1	firstDerivativeCoefficient()	Retrieve the R2 to R1 First Derivative Coefficient Function
java.util.TreeSet<java.lang.Double>	orderedRegularSingularPoints()	Retrieve the Ordered Regular Singular Points of the Second Order ODE
R2ToR1	secondDerivativeCoefficient()	Retrieve the R2 to R1 Second Derivative Coefficient Function
R2ToR1	zeroDerivativeCoefficient()	Retrieve the R2 to R1 Zero Derivative Coefficient Function

Methods inherited from class java.lang.Object

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

Constructor Details

SecondOrder

public SecondOrder(R2ToR1 secondDerivativeCoefficient,
R2ToR1 firstDerivativeCoefficient,
R2ToR1 zeroDerivativeCoefficient)
            throws java.lang.Exception

SecondOrder Constructor

Parameters:

secondDerivativeCoefficient - Second Order Derivative Coefficient Term

firstDerivativeCoefficient - First Order Derivative Coefficient Term

zeroDerivativeCoefficient - Zero Order Derivative Coefficient Term

Throws:

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

Method Details

secondDerivativeCoefficient

public R2ToR1 secondDerivativeCoefficient()

Retrieve the R² to R¹ Second Derivative Coefficient Function

Returns:

The R² to R¹ Second Derivative Coefficient Function

firstDerivativeCoefficient

public R2ToR1 firstDerivativeCoefficient()

Retrieve the R² to R¹ First Derivative Coefficient Function

Returns:

The R² to R¹ First Derivative Coefficient Function

zeroDerivativeCoefficient

public R2ToR1 zeroDerivativeCoefficient()

Retrieve the R² to R¹ Zero Derivative Coefficient Function

Returns:

The R² to R¹ Zero Derivative Coefficient Function

orderedRegularSingularPoints

public java.util.TreeSet<java.lang.Double> orderedRegularSingularPoints()

Retrieve the Ordered Regular Singular Points of the Second Order ODE

Returns:

The Ordered Regular Singular Points of the Second Order ODE