Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b85j)

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.b85j.01

Input Form

Hypergeometric2F1[-(43/8), 33/8, 11/2, -z] == -((1024 (4 Sqrt[z] (-1372560 - 1495110 z + 1575993 z^2 - 4524546 z^3 - 9525116 z^4 + 157007168 z^5 + 571434475 z^6 + 851912768 z^7 + 660684544 z^8 + 264536064 z^9 + 43450368 z^10) Cos[(5 ArcTan[Sqrt[z]])/4] - (-4392192 - 3960816 z + 5806419 z^2 - 15519732 z^3 + 134682450 z^4 + 1359518428 z^5 + 3679493939 z^6 + 4886587744 z^7 + 3552443648 z^8 + 1363415040 z^9 + 217251840 z^10) Sin[(5 ArcTan[Sqrt[z]])/4]))/(207699334895 z^(9/2) (1 + z)^(5/8)))

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]