Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cbg7)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=31/8, b>=a

For fixed z and a=31/8, b=35/8

http://functions.wolfram.com/07.23.03.cbg7.01

Input Form

Hypergeometric2F1[31/8, 35/8, -(21/4), z] == (-29376 + 482256 z - 3904776 z^2 + 21416805 z^3 - 95571654 z^4 + 442162347 z^5 - 5844341052 z^6 - 11536760213 z^7 - 4123508950 z^8 - 250895787 z^9 + (1/Sqrt[1 - z]) (-29376 + 496944 z - 4142232 z^2 + 23310747 z^3 - 105820953 z^4 + 487497087 z^5 - 6054674373 z^6 - 14910495391 z^7 - 7179336219 z^8 - 769169259 z^9 - 8904175 z^10))/ (29376 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + z)^13)

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]