Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4oz)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-35/8

http://functions.wolfram.com/07.23.03.b4oz.01

Input Form

Hypergeometric2F1[-(47/8), -(35/8), 11/2, -z] == -((1024 (4 Sqrt[z] (-112 - 2922 z - 42875 z^2 - 547484 z^3 - 240599216 z^4 + 1199640208 z^5 - 1624709534 z^6 + 724138716 z^7 - 95875672 z^8 + 2000922 z^9 + 16401 z^10) Cos[ArcTan[Sqrt[z]]/4] + (1792 + 47312 z + 700463 z^2 + 8970360 z^3 + 193768036 z^4 - 2609597848 z^5 + 6437836314 z^6 - 4987089464 z^7 + 1248856036 z^8 - 76945912 z^9 - 16401 z^10) Sin[ArcTan[Sqrt[z]]/4]))/ (936576640945 z^(9/2) (1 + z)^(1/8)))

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]