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

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=37/8

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

Input Form

Hypergeometric2F1[-(31/8), 37/8, 17/4, z] == (1/(1035006665 z^4)) (8 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (4 (21390 + 89125 z + 523342 z^2 + 12391227 z^3 - 69474156 z^4 + 125168736 z^5 - 95107584 z^6 + 26357760 z^7) + (1/Sqrt[1 - z]) (-85560 - 313720 z - 1904423 z^2 - 48468314 z^3 + 367654289 z^4 - 926278752 z^5 + 1096136448 z^6 - 627314688 z^7 + 140574720 z^8)))

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]