Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9qz)

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=-39/8, b>=a

For fixed z and a=-39/8, b=-27/8

http://functions.wolfram.com/07.23.03.b9qz.01

Input Form

Hypergeometric2F1[-(39/8), -(27/8), 17/4, z] == (1/(48556173925 z^4)) (8 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-154008 + 3713304 z - 59748687 z^2 + 2241855954 z^3 + 14917845455 z^4 + 20549204916 z^5 + 7651901727 z^6 + 616156994 z^7 - 1535463 z^8 - (1/Sqrt[1 - z]) (4 (-38502 + 947577 z - 15396522 z^2 + 567818940 z^3 + 2692349782 z^4 + 503366314 z^5 - 2713555574 z^6 - 995058156 z^7 - 40945680 z^8 + 511821 z^9))))

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]