Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5o6)

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=39/8

http://functions.wolfram.com/07.23.03.b5o6.01

Input Form

Hypergeometric2F1[-(47/8), 39/8, 11/2, z] == (1/(751899556815 z^(9/2))) (1024 (Sqrt[z] (273728 + 347048 z + 851123 z^2 + 3622619 z^3 + 778047325 z^4 - 4321009583 z^5 + 10009363628 z^6 - 12455560656 z^7 + 8779364352 z^8 - 3320190720 z^9 + 525837312 z^10) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-1094912 - 635440 z - 2360293 z^2 - 11992708 z^3 - 164758594 z^4 + 2202912976 z^5 - 8202140001 z^6 + 15326694812 z^7 - 16463083824 z^8 + 10373730048 z^9 - 3583109376 z^10 + 525837312 z^11) Sin[ArcSin[Sqrt[z]]/4])))

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]