Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5te)

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=47/8

http://functions.wolfram.com/07.23.03.b5te.01

Input Form

Hypergeometric2F1[-(47/8), 47/8, 9/2, -z] == (1/(7411934295 z^(7/2) Sqrt[1 + z])) (256 (Sqrt[z] Sqrt[1 + z] (-752 + 6815 z - 64202 z^2 + 30320599 z^3 + 246016104 z^4 + 785983032 z^5 + 1291392000 z^6 + 1162296576 z^7 + 546674688 z^8 + 105412608 z^9) Cosh[ArcSinh[Sqrt[z]]/4] - 4 (-752 + 6298 z - 59455 z^2 + 1323003 z^3 + 25794229 z^4 + 132938763 z^5 + 329110362 z^6 + 452698560 z^7 + 355614336 z^8 + 149845248 z^9 + 26353152 z^10) Sinh[ArcSinh[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]