Package org.drip.specialfunction.group

Class MonodromyTransform2F1

java.lang.Object
org.drip.specialfunction.group.MonodromyTransform2F1
public class MonodromyTransform2F1
extends java.lang.Object
MonodromyTransform2F1 builds out the Monodromy Loop Solution Transformation Matrices for Paths around the Singular Points. 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:
  • Generate the Monodromy Group Matrix G0 around the '0' Singularity
  • Generate the "Mu" Intermediate for the G1 Monodromy Matrix
  • Generate the Monodromy Group Matrix G1 around the '1' Singularity

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

  • Constructor Details

    • MonodromyTransform2F1

      public MonodromyTransform2F1()

  • Method Details

    • G0

      public static final CartesianComplexNumber[][] G0​(FundamentalGroupPathExponent2F1 pathExponent1, FundamentalGroupPathExponent2F1 pathExponent2)
      Generate the Monodromy Group Matrix G0 around the '0' Singularity
      Parameters:
      pathExponent1 - Path Monodromy Exponents of the Fundamental Group #1
      pathExponent2 - Path Monodromy Exponents of the Fundamental Group #2
      Returns:
      The Monodromy Group Matrix G0 around the '0' Singularity

    • G1Mu

      public static final double G1Mu​(FundamentalGroupPathExponent2F1 pathExponent1, FundamentalGroupPathExponent2F1 pathExponent2) throws java.lang.Exception
      Compute the "Mu" Intermediate for the G1 Monodromy Matrix
      Parameters:
      pathExponent1 - Path Monodromy Exponents of the Fundamental Group #1
      pathExponent2 - Path Monodromy Exponents of the Fundamental Group #2
      Returns:
      The "Mu" Intermediate for the G1 Monodromy Matrix
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • G1

      public static final CartesianComplexNumber[][] G1​(FundamentalGroupPathExponent2F1 pathExponent1, FundamentalGroupPathExponent2F1 pathExponent2)
      Generate the Monodromy Group Matrix G1 around the '1' Singularity
      Parameters:
      pathExponent1 - Path Monodromy Exponents of the Fundamental Group #1
      pathExponent2 - Path Monodromy Exponents of the Fundamental Group #2
      Returns:
      The Monodromy Group Matrix G1 around the '1' Singularity