Package org.drip.specialfunction.group

Class Kummer24

java.lang.Object
org.drip.specialfunction.group.FuchsianEquation
org.drip.specialfunction.group.Kummer24
public class Kummer24
extends FuchsianEquation
Kummer24 contains the Isomorphic Klein-4 Group of the Transformations built out of the Solutions emanating from the Singularities of the Hyper-geometric 2F1 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:
  • Construct the Kummer24 Isomorphic Array Version of the Fuchsian Equation
  • Generate the Transposition (12) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
  • Generate the Transposition (23) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
  • Generate the Transposition (34) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3

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

  • Method Details

    • Standard

      public static final Kummer24 Standard​(RegularHypergeometricEstimator regularHypergeometricEstimator)
      Construct the Kummer24 Isomorphic Array Version of the Fuchsian Equation
      Parameters:
      regularHypergeometricEstimator - The Regular Hyper-geometric Estimator
      Returns:
      The Kummer24 Isomorphic Array Version of the Fuchsian Equation

    • transposition12

      public RegularHypergeometricEstimator transposition12()
      Generate the Transposition (12) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
      Returns:
      The Transposition (12) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3

    • transposition23

      public RegularHypergeometricEstimator transposition23()
      Generate the Transposition (23) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
      Returns:
      The Transposition (23) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3

    • transposition34

      public RegularHypergeometricEstimator transposition34()
      Generate the Transposition (34) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3
      Returns:
      The Transposition (34) under the Fuchsian Isomorphism with Symmetry Group on points 1, 2, 3