Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6fm)

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=-11/8

http://functions.wolfram.com/07.23.03.b6fm.01

Input Form

Hypergeometric2F1[-(45/8), -(11/8), 9/2, -z] == (256 (Sqrt[z] Sqrt[1 + z] (257520 + 4563469 z + 47763522 z^2 + 1878451299 z^3 - 5578601272 z^4 + 2190218355 z^5 + 138260682 z^6 + 19990381 z^7 + 2370012 z^8 + 148304 z^9) Cosh[(3 ArcSinh[Sqrt[z]])/4] - (343360 + 6377912 z + 68870505 z^2 + 925340178 z^3 - 3429137457 z^4 - 2163757352 z^5 + 2256992231 z^6 + 147968890 z^7 + 21156849 z^8 + 2444164 z^9 + 148304 z^10) Sinh[(3 ArcSinh[Sqrt[z]])/4]))/ (313624632685 z^(7/2) 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]