Package org.drip.specialfunction.group

Class RiemannSphereSpanner

java.lang.Object
org.drip.specialfunction.group.RiemannSphereSpanner
public class RiemannSphereSpanner
extends java.lang.Object
RiemannSphereSpanner determines the Conformality and Tile Scheme of the Schwarz Singular Triangle Maps over the Riemann Sphere. 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:
  • Schwarz Triangle Tiles Nothing
  • Schwarz Triangle Riemann Nothing
  • Schwarz Triangle Complex Nothing
  • Schwarz Triangle Upper Half Nothing
  • RiemannSphereSpanner Constructor
  • Retrieve the Schwarz Triangle Map Array
  • Indicate if the Spanner is Conformal
  • Indicate how the Schwarz Triangle Tiles the Riemann Sphere

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

  • Field Details

    • SCHWARZ_TRIANGLE_TILES_NOTHING

      public static final int SCHWARZ_TRIANGLE_TILES_NOTHING
      Schwarz Triangle Tiles Nothing
      See Also:
      Constant Field Values

    • SCHWARZ_TRIANGLE_TILES_RIEMANN_SPHERE

      public static final int SCHWARZ_TRIANGLE_TILES_RIEMANN_SPHERE
      Schwarz Triangle Tiles the Riemann Sphere
      See Also:
      Constant Field Values

    • SCHWARZ_TRIANGLE_TILES_COMPLEX_PLANE

      public static final int SCHWARZ_TRIANGLE_TILES_COMPLEX_PLANE
      Schwarz Triangle Tiles the Complex Plane
      See Also:
      Constant Field Values

    • SCHWARZ_TRIANGLE_TILES_UPPER_HALF_PLANE

      public static final int SCHWARZ_TRIANGLE_TILES_UPPER_HALF_PLANE
      Schwarz Triangle Tiles the Upper Half Plane
      See Also:
      Constant Field Values

  • Constructor Details

    • RiemannSphereSpanner

      public RiemannSphereSpanner​(SchwarzTriangleMap[] schwarzTriangleMapArray) throws java.lang.Exception
      RiemannSphereSpanner Constructor
      Parameters:
      schwarzTriangleMapArray - The Schwarz Triangle Map Array
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • schwarzTriangleMapArray

      public SchwarzTriangleMap[] schwarzTriangleMapArray()
      Retrieve the Schwarz Triangle Map Array
      Returns:
      The Schwarz Triangle Map Array

    • isConformal

      public boolean isConformal()
      Indicate if the Spanner is Conformal
      Returns:
      TRUE - The Spanner is Conformal

    • tileIndicator

      public int tileIndicator() throws java.lang.Exception
      Indicate how the Schwarz Triangle Tiles the Riemann Sphere
      Returns:
      Indicator of how the Schwarz Triangle Tiles the Riemann Sphere
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid