Package org.drip.specialfunction.group

Class FundamentalGroupPathExponent2F1

java.lang.Object
org.drip.specialfunction.group.FundamentalGroupPathExponent2F1
public class FundamentalGroupPathExponent2F1
extends java.lang.Object
FundamentalGroupPathExponent2F1 holds the Exponents of the Monodromy Loop Paths around the Singular Points 0, 1, and Infinity. 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:
  • FundamentalGroupPathExponent2F1 Constructor
  • Retrieve the Exponent corresponding to the Loop around 0
  • Retrieve the Exponent corresponding to the Loop around 1
  • Retrieve the Exponent corresponding to the Loop around Infinity

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
    FundamentalGroupPathExponent2F1​(double alpha, double beta, double gamma)
    FundamentalGroupPathExponent2F1 Constructor

  • Method Summary

    Modifier and Type Method Description
    double alpha()
    Retrieve the Exponent corresponding to the Loop around 0
    double beta()
    Retrieve the Exponent corresponding to the Loop around 1
    double gamma()
    Retrieve the Exponent corresponding to the Loop around Infinity

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • FundamentalGroupPathExponent2F1

      public FundamentalGroupPathExponent2F1​(double alpha, double beta, double gamma) throws java.lang.Exception
      FundamentalGroupPathExponent2F1 Constructor
      Parameters:
      alpha - Exponent corresponding to the Loop around 0
      beta - Exponent corresponding to the Loop around 1
      gamma - Exponent corresponding to the Loop around Infinity
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • alpha

      public double alpha()
      Retrieve the Exponent corresponding to the Loop around 0
      Returns:
      Exponent corresponding to the Loop around 0

    • beta

      public double beta()
      Retrieve the Exponent corresponding to the Loop around 1
      Returns:
      Exponent corresponding to the Loop around 1

    • gamma

      public double gamma()
      Retrieve the Exponent corresponding to the Loop around Infinity
      Returns:
      Exponent corresponding to the Loop around Infinity