Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bi90)

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=-27/8, b>=a

For fixed z and a=-27/8, b=41/8

http://functions.wolfram.com/07.23.03.bi90.01

Input Form

Hypergeometric2F1[-(27/8), 41/8, 7/2, -z] == -((64 (Sqrt[z] (1140 - 11685 z - 104797 z^2 + 990304 z^3 + 4492544 z^4 + 5705728 z^5 + 2293760 z^6) Cos[(5 ArcTan[Sqrt[z]])/4] - (912 - 9519 z + 167181 z^2 + 2343152 z^3 + 6966400 z^4 + 7669760 z^5 + 2867200 z^6) Sin[(5 ArcTan[Sqrt[z]])/4]))/ (19939045 z^(5/2) (1 + z)^(5/8)))

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]