Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7ah)

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=45/8

http://functions.wolfram.com/07.23.03.b7ah.01

Input Form

Hypergeometric2F1[-(45/8), 45/8, 11/2, z] == (1/(43546758255 z^(9/2))) (1024 (4 Sqrt[z] (1680 + 5590 z + 21654 z^2 + 121383 z^3 + 12399154 z^4 - 86094783 z^5 + 235943850 z^6 - 337492160 z^7 + 268202880 z^8 - 112738560 z^9 + 19627520 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((-8960 - 22160 z - 89723 z^2 - 547575 z^3 - 8869857 z^4 + 157001307 z^5 - 699102832 z^6 + 1509776120 z^7 - 1834912000 z^8 + 1288474880 z^9 - 490209280 z^10 + 78510080 z^11) Sin[(3 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]