Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9uo)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-19/4, b>=a

For fixed z and a=-19/4, b=21/4

http://functions.wolfram.com/07.23.03.a9uo.01

Input Form

Hypergeometric2F1[-(19/4), 21/4, 1, z] == (1/(14549535 Pi)) (2 (8 Sqrt[1 - z] (7759469 - 143669760 z + 646797312 z^2 - 1027604480 z^3 + 528482304 z^4) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (16488341 + 31037876 Sqrt[1 - z] - 192 (1219891 + 2993120 Sqrt[1 - z]) z + 129024 (6725 + 20052 Sqrt[1 - z]) z^2 - 1835008 (641 + 2240 Sqrt[1 - z]) z^3 + 528482304 (1 + 4 Sqrt[1 - z]) z^4) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]