Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b853)

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=-43/8, b>=a

For fixed z and a=-43/8, b=33/8

http://functions.wolfram.com/07.23.03.b853.01

Input Form

Hypergeometric2F1[-(43/8), 33/8, 9/4, z] == (2 2^(1/4) (-188727 + 32739750 z - 259338191 z^2 + 745439904 z^3 - 1001851136 z^4 + 642543616 z^5 - 159318016 z^6 + (1/Sqrt[1 - z]) (188727 + 61426254 z - 706194353 z^2 + 2844703276 z^3 - 5551220224 z^4 + 5722123264 z^5 - 3008299008 z^6 + 637272064 z^7)))/ (188520735 (1 + Sqrt[1 - z])^(1/4) z)

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]