Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bko9)

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=-23/8, b>=a

For fixed z and a=-23/8, b=45/8

http://functions.wolfram.com/07.23.03.bko9.01

Input Form

Hypergeometric2F1[-(23/8), 45/8, -(23/4), z] == (1/(14352448 2^(3/4) (-1 + z)^8)) ((1 + Sqrt[1 - z])^(3/4) (2 (3588112 - 17940560 z + 29755363 z^2 - 11378092 z^3 - 8847958 z^4 - 8983156 z^5 + 148771035 z^6 - 259963464 z^7 + 203362368 z^8 - 78363648 z^9 + 12165120 z^10) + (1/Sqrt[1 - z]) (7176224 - 39469232 z + 76554258 z^2 - 48474921 z^3 - 11794416 z^4 - 8787870 z^5 - 347144714 z^6 + 974069471 z^7 - 1150040736 z^8 + 719710464 z^9 - 236679168 z^10 + 32440320 z^11)))

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]