Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4ov)

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=-35/8

http://functions.wolfram.com/07.23.03.b4ov.01

Input Form

Hypergeometric2F1[-(47/8), -(35/8), 9/2, -z] == -((256 (Sqrt[z] (-16 - 469 z - 8967 z^2 - 5847413 z^3 + 35517053 z^4 - 56756427 z^5 + 29158507 z^6 - 4371911 z^7 + 101871 z^8 + 924 z^9) Cos[ArcTan[Sqrt[z]]/4] + (64 + 1896 z + 36449 z^2 + 1051127 z^3 - 17581707 z^4 + 51934883 z^5 - 46878013 z^6 + 13404453 z^7 - 928409 z^8 - 231 z^9) Sin[ArcTan[Sqrt[z]]/4]))/ (1430373285 z^(7/2) (1 + z)^(1/8)))

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]