Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5o7)

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.b5o7.01

Input Form

Hypergeometric2F1[-(47/8), 39/8, 11/2, -z] == (1024 (Sqrt[z] Sqrt[1 + 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) Cosh[ArcSinh[Sqrt[z]]/4] - (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) Sinh[ArcSinh[Sqrt[z]]/4]))/ (751899556815 z^(9/2) Sqrt[1 + 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]