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

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=45/8

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

Input Form

Hypergeometric2F1[-(31/8), 45/8, -(15/4), z] == (1/(17185168 2^(3/4) (-1 + z)^5)) ((1 + Sqrt[1 - z])^(3/4) (-8592584 - 8592584 z - 11228945 z^2 - 22513686 z^3 + 2789163735 z^4 - 8915209248 z^5 + 11247405312 z^6 - 6492794880 z^7 + 1433862144 z^8 + (1/Sqrt[1 - z]) (4 (-2148146 - 1074073 z - 1464645 z^2 - 3822026 z^3 - 747985087 z^4 + 3375674073 z^5 - 6110254656 z^6 + 5581804800 z^7 - 2572517376 z^8 + 477954048 z^9))))

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]