Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ba0b)

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=-3/8

http://functions.wolfram.com/07.23.03.ba0b.01

Input Form

Hypergeometric2F1[-(39/8), -(3/8), 11/2, -z] == -((1024 (Sqrt[z] (-448 - 5752 z - 36741 z^2 - 171229 z^3 - 9880706 z^4 + 4338894 z^5 + 729031 z^6 + 154007 z^7 + 23568 z^8 + 1792 z^9) Cos[ArcTan[Sqrt[z]]/4] + (1792 + 23568 z + 154007 z^2 + 729031 z^3 + 4338894 z^4 - 9880706 z^5 - 171229 z^6 - 36741 z^7 - 5752 z^8 - 448 z^9) Sin[ArcTan[Sqrt[z]]/4]))/(9059030805 z^(9/2) (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]