Package org.drip.sample.hypergeometric

Estimates of Hyper-geometric Function

Author:

Lakshmi Krishnamurthy

Class Summary

Class	Description
DerivativeEstimate	DerivativeEstimate estimates the Hyper-geometric Function Derivative using the Euler Integral Representation.
EllipticEIntegralEstimate	EllipticEIntegralEstimate estimates the Elliptic E-Integral Function using the 2F1 Hyper-geometric Function.
EllipticKIntegralEstimate	EllipticKIntegralEstimate estimates the Elliptic K-Integral Function using the 2F1 Hyper-geometric Function.
EulerQuadratureEstimate	EulerQuadratureEstimate estimates the Hyper-geometric Function using the Euler Integral Representation.
FirstOrderSpecialCaseProperty	FirstOrderSpecialCaseProperty verifies the First-Order Derivative Special Case (c = a + 1) Identity Lemma.
FirstOrderSwitchProperty	FirstOrderSwitchProperty verifies the First-Order Derivative Parameter Switch Identity Lemma.
GaussBaileyProperty	GaussBaileyProperty verifies the Gauss Bailey Identity Property Lemma for z = +0.5.
GaussContiguousProperty2	GaussContiguousProperty2 verifies the Gauss Contiguous Identity #2 Lemma for Hyper-geometric Functions.
GaussContiguousProperty3	GaussContiguousProperty3 verifies the Gauss Contiguous Identity #3 Lemma for Hyper-geometric Functions.
GaussContiguousProperty4	GaussContiguousProperty4 verifies the Gauss Contiguous Identity #4 Lemma for Hyper-geometric Functions.
GaussContiguousProperty5	GaussContiguousProperty5 verifies the Gauss Contiguous Identity #5 Lemma for Hyper-geometric Functions.
GaussContiguousProperty6	GaussContiguousProperty6 verifies the Gauss Contiguous Identity #6 Lemma for Hyper-geometric Functions.
GaussContiguousProperty7	GaussContiguousProperty7 verifies the Gauss Contiguous Identity #7 Lemma for Hyper-geometric Functions.
GaussContinuedFractionProperty	GaussContinuedFractionProperty verifies the Gauss Continued Fraction Identity Property Lemma for Rational Z.
GaussDougallProperty	GaussDougallProperty verifies the Gauss Dougall Identity Property Lemma for z = 1.
GaussKummerProperty	GaussKummerProperty verifies the Gauss Kummer Identity Property Lemma for z = -1.
GaussSecondSummationProperty	GaussSecondSummationProperty verifies the Gauss Second Summation Identity Property Lemma for z = +0.5.
GaussVanderMondeProperty	GaussVanderMondeProperty verifies the Gauss van der Monde Identity Property Lemma for z = 1.
GesselStantonKoepfProperty1	GesselStantonKoepfProperty1 verifies the First Gessel-Stanton-Koepf Identity Property Lemma for Rational Z.
GesselStantonKoepfProperty2	GesselStantonKoepfProperty2 verifies the Second Gessel-Stanton-Koepf Identity Property Lemma for Rational Z.
GoursatCubicTransformationProperty	GoursatCubicTransformationProperty verifies the Goursat Cubic Transformation Identity Lemma.
GoursatQuadraticTransformationProperty	GoursatQuadraticTransformationProperty verifies the Goursat Quadratic Transformation Identity Lemma.
IncompleteBetaProperty	IncompleteBetaProperty verifies the Incomplete Beta Identity Property Lemma for Rational Z.
InversePowerAProperty	InversePowerAProperty verifies the Hyper-geometric Function Special Case ((1.
InverseSineProperty	InverseSineProperty verifies the Hyper-geometric Function Special Case (arcsin (z) = 2F1 (0.5, 0.5; 1.5, z * z)) Identity Lemma.
JacobiEstimate	JacobiEstimate estimates the Jacobi Hyper-geometric Function.
KummerConfluentEstimate	KummerConfluentEstimate estimates the Kummer's Confluent Hyper-geometric Function.
KummerEulerTransformation	KummerEulerTransformation reconciles the Hyper-geometric Function Estimates using the Euler Integral Representation against Euler Transformation.
KummerPfaffFirstTransformation	KummerPfaffFirstTransformation reconciles the Hyper-geometric Function Estimates using the Euler Integral Representation against First Pfaff Transformation.
KummerPfaffSecondTransformation	KummerPfaffSecondTransformation reconciles the Hyper-geometric Function Estimates using the Euler Integral Representation against Second Pfaff Transformation.
LegendreEstimate	LegendreEstimate estimates the Legendre Hyper-geometric Function.
LogOnePlusZProperty	LogOnePlusZProperty verifies the Hyper-geometric Function Special Case (log (1 + z) = 2F1 (1, 1,; 2, -z)) Identity Lemma.
PochhammerSeriesEstimate	PochhammerSeriesEstimate estimates the Hyper-geometric Function using the Pochhammer Series and compares it against the Euler Integral Representation.
VidunasHigherOrderTransformationProperty	VidunasHigherOrderTransformationProperty verifies the Vidunas Higher-Order Transformation Identity Lemma.