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

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=-25/8, b>=a

For fixed z and a=-25/8, b=27/8

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

Input Form

Hypergeometric2F1[-(25/8), 27/8, 11/2, -z] == -((1024 (Sqrt[z] (1332800 + 3308200 z + 637245 z^2 - 587265 z^3 - 6655657 z^4 - 832179 z^5 + 11214560 z^6 + 10434816 z^7 + 2838528 z^8) Cos[(7 ArcTan[Sqrt[z]])/4] - (761600 + 1366800 z - 902785 z^2 - 512295 z^3 + 1686825 z^4 + 21252931 z^5 + 34314308 z^6 + 21676032 z^7 + 4967424 z^8) Sin[(7 ArcTan[Sqrt[z]])/4]))/ (9425297453 z^(9/2) (1 + z)^(7/8)))

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]