Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b51b)

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=-1/8

http://functions.wolfram.com/07.23.03.b51b.01

Input Form

Hypergeometric2F1[-(47/8), -(1/8), 9/2, z] == (1/(2364407040105 z^(7/2))) (256 ((-Sqrt[z]) (536176 - 7204865 z + 52310671 z^2 - 9654846348 z^3 - 2132016722 z^4 + 794162071 z^5 - 301896525 z^6 + 86653798 z^7 - 15827504 z^8 + 1357664 z^9) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) (2 (-1072352 + 15146972 z - 114440065 z^2 + 908550232 z^3 + 104345859 z^4 - 1248097708 z^5 + 467607397 z^6 - 171664920 z^7 + 47198921 z^8 - 8253168 z^9 + 678832 z^10) 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]