Package org.drip.specialfunction.group

Class FuchsianEquation

java.lang.Object
org.drip.specialfunction.group.FuchsianEquation
Direct Known Subclasses:
Kummer24
public class FuchsianEquation
extends java.lang.Object
FuchsianEquation holds the Isomorphic Order, Coexter Singularity Index, and the Klein-4 Transformations of the 2F1 Regular Hyper-geometric Function. 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:
  • FuchsianEquation Constructor
  • Retrieve the Coxeter Singularity Index
  • Retrieve the Isomorphy Order
  • Retrieve the Klein Group of Isomorphic Functions

Module Computational Core Module
Library Function Analysis Library
Project Special Function Implementation and Analysis
Package Special Function Singularity Solution Group
Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    FuchsianEquation​(R1ToR1[] kleinGroupFunctionArray)
    FuchsianEquation Constructor

  • Method Summary

    Modifier and Type Method Description
    int coxeterSingularityIndex()
    Retrieve the Coxeter Singularity Index
    int isomorphyOrder()
    Retrieve the Isomorphy Order
    R1ToR1[] kleinGroupFunctionArray()
    Retrieve the Klein Group of Isomorphic Functions

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • FuchsianEquation

      public FuchsianEquation​(R1ToR1[] kleinGroupFunctionArray) throws java.lang.Exception
      FuchsianEquation Constructor
      Parameters:
      kleinGroupFunctionArray - Array of the Klein Group Isomorphic Functions
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • coxeterSingularityIndex

      public int coxeterSingularityIndex()
      Retrieve the Coxeter Singularity Index
      Returns:
      The Coxeter Singularity Index

    • isomorphyOrder

      public int isomorphyOrder()
      Retrieve the Isomorphy Order
      Returns:
      The Isomorphy Order

    • kleinGroupFunctionArray

      public R1ToR1[] kleinGroupFunctionArray()
      Retrieve the Klein Group of Isomorphic Functions
      Returns:
      The Klein Group of Isomorphic Functions