Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b64z)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-43/8

http://functions.wolfram.com/07.23.03.b64z.01

Input Form

Hypergeometric2F1[-(45/8), -(43/8), 11/2, z] == (1024 (Sqrt[z] (310054080 - 8834695720 z + 142824335697 z^2 - 2029637261736 z^3 + 190049613557852 z^4 + 1454141956559256 z^5 + 3021989588263590 z^6 + 2238990446916008 z^7 + 596718582086556 z^8 + 47981100280848 z^9 + 622346151889 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((-413405440 + 12132711440 z - 200480368321 z^2 + 2868457708185 z^3 - 68725963388964 z^4 - 801768355008396 z^5 - 1375134689622014 z^6 + 351636789108766 z^7 + 1342722141685420 z^8 + 501974865773044 z^9 + 45993168654391 z^10 + 622346151889 z^11) Sin[(3 ArcSin[Sqrt[z]])/4])))/(143599789257709785 z^(9/2))

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]