Package org.drip.specialfunction.property

Class HypergeometricEqualityLemma

java.lang.Object
org.drip.specialfunction.property.HypergeometricEqualityLemma
public class HypergeometricEqualityLemma
extends java.lang.Object
HypergeometricEqualityLemma verifies the Hyper-geometric Equality Lemma Properties. 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 First-Order Derivative Switch Verifier
  • Construct the First-Order Derivative Special Case Verifier
  • Construct the Log (1 + z) Special Case Verifier
  • Construct the Inverse Power A Special Case Verifier
  • Construct the Inverse Sine Special Case Verifier
  • Construct the Goursat Quadratic Transformation Verifier
  • Construct the Goursat Cubic Transformation Verifier
  • Construct the Vidunas Higher Order Transformation Verifier
  • Construct the Gauss Van der Monde z = +1 Verifier
  • Construct the Gauss-Dougall z = +1 Verifier
  • Construct the Gauss Kummer z = -1 Verifier
  • Construct the Gauss Second Summation z = 0.5 Verifier
  • Construct the Gauss Bailey z = +0.5 Verifier
  • Construct the First Gessel Stanton Koepf Rational Z Verifier
  • Construct the Second Gessel Stanton Koepf Rational Z Verifier
  • Construct the Incomplete Beta Verifier

Module Computational Core Module
Library Function Analysis Library
Project Special Function Implementation and Analysis
Package Special Function Property Lemma Verifiers
Author:
Lakshmi Krishnamurthy

  • Constructor Details

    • HypergeometricEqualityLemma

      public HypergeometricEqualityLemma()

  • Method Details

    • FirstOrderDerivativeSwitch

      public static final R1ToR1Property FirstOrderDerivativeSwitch​(double a, double b)
      Construct the First-Order Derivative Switch Verifier
      Parameters:
      a - A
      b - B
      Returns:
      The First-Order Derivative Switch Verifier

    • FirstOrderDerivativeSpecialCase

      public static final R1ToR1Property FirstOrderDerivativeSpecialCase​(double a, double b)
      Construct the First-Order Derivative Special Case Verifier
      Parameters:
      a - A
      b - B
      Returns:
      The First-Order Derivative Special Case Verifier

    • LogOnePlusZ

      public static final R1ToR1Property LogOnePlusZ()
      Construct the Log (1 + z) Special Case Verifier
      Returns:
      The Log (1 + z) Special Case Verifier

    • InversePowerA

      public static final R1ToR1Property InversePowerA​(double a)
      Construct the Inverse Power A Special Case Verifier
      Parameters:
      a - A
      Returns:
      The Inverse Power A Special Case Verifier

    • InverseSine

      public static final R1ToR1Property InverseSine()
      Construct the Inverse Sine Special Case Verifier
      Returns:
      The Inverse Sine Special Case Verifier

    • GoursatQuadraticTransformation

      public static final R1ToR1Property GoursatQuadraticTransformation​(double a, double b)
      Construct the Goursat Quadratic Transformation Verifier
      Parameters:
      a - A
      b - B
      Returns:
      The Goursat Quadratic Transformation Verifier

    • GoursatCubicTransformation

      public static final R1ToR1Property GoursatCubicTransformation​(double a)
      Construct the Goursat Cubic Transformation Verifier
      Parameters:
      a - A
      Returns:
      The Goursat Cubic Transformation Verifier

    • VidunasHigherOrderTransformation

      public static final R1ToR1Property VidunasHigherOrderTransformation()
      Construct the Vidunas Higher Order Transformation Verifier
      Returns:
      The Vidunas Higher Order Transformation Verifier

    • GaussVanderMondeZPlusOne

      public static final R3ToR1Property GaussVanderMondeZPlusOne()
      Construct the Gauss Van der Monde z = +1 Verifier
      Returns:
      The Gauss Van der Monde z = +1 Verifier

    • GaussDougallZPlusOne

      public static final R3ToR1Property GaussDougallZPlusOne()
      Construct the Gauss-Dougall z = +1 Verifier
      Returns:
      The Gauss-Dougall z = +1 Verifier

    • GaussKummerZMinusOne

      public static final R2ToR1Property GaussKummerZMinusOne()
      Construct the Gauss Kummer z = -1 Verifier
      Returns:
      The Gauss Kummer z = -1 Verifier

    • GaussSecondSummationZPlusHalf

      public static final R2ToR1Property GaussSecondSummationZPlusHalf()
      Construct the Gauss Second Summation z = 0.5 Verifier
      Returns:
      The Gauss Second Summation z = 0.5 Verifier

    • GaussBaileyZPlusHalf

      public static final R2ToR1Property GaussBaileyZPlusHalf()
      Construct the Gauss Bailey z = +0.5 Verifier
      Returns:
      The Gauss Bailey z = +0.5 Verifier

    • FirstGesselStantonKoepf

      public static final R2ToR1Property FirstGesselStantonKoepf()
      Construct the First Gessel Stanton Koepf Rational Z Verifier
      Returns:
      The First Gessel Stanton Koepf Rational Z Verifier

    • SecondGesselStantonKoepf

      public static final R2ToR1Property SecondGesselStantonKoepf()
      Construct the Second Gessel Stanton Koepf Rational Z Verifier
      Returns:
      The Second Gessel Stanton Koepf Rational Z Verifier

    • GaussContinuedFractionRecursive

      public static final R1ToR1Property GaussContinuedFractionRecursive​(double a, double b, double c)
      Construct the Gauss Continued Fraction Recursive Verifier
      Parameters:
      a - A
      b - B
      c - C
      Returns:
      The Gauss Continued Fraction Recursive Verifier

    • IncompleteBeta

      public static final R1ToR1Property IncompleteBeta​(double p, double q)
      Construct the Incomplete Beta Verifier
      Parameters:
      p - P
      q - Q
      Returns:
      The Incomplete Beta Verifier