Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.brp3)

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=-11/8, b>=a

For fixed z and a=-11/8, b=41/8

http://functions.wolfram.com/07.23.03.brp3.01

Input Form

Hypergeometric2F1[-(11/8), 41/8, -(11/4), z] == (4 (170 - 595 z + 255 z^2 + 850 z^3 - 2599 z^4 + 2751 z^5 - 1344 z^6 + 256 z^7) + (1/Sqrt[1 - z]) (680 - 2720 z + 2125 z^2 + 3145 z^3 - 39329 z^4 + 70243 z^5 - 58464 z^6 + 24320 z^7 - 4096 z^8))/ (680 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + z)^6)

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]