Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8a0)

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=-43/8, b>=a

For fixed z and a=-43/8, b=41/8

http://functions.wolfram.com/07.23.03.b8a0.01

Input Form

Hypergeometric2F1[-(43/8), 41/8, 11/2, -z] == -((1024 (Sqrt[z] (5490240 - 9509880 z + 27581103 z^2 - 127317195 z^3 - 636913219 z^4 + 6598503359 z^5 + 32139069840 z^6 + 57986143488 z^7 + 52418396160 z^8 + 23912185856 z^9 + 4402970624 z^10) Cos[(5 ArcTan[Sqrt[z]])/4] - (4392192 - 8431440 z + 23625189 z^2 - 106272909 z^3 + 1295267715 z^4 + 16486085057 z^5 + 54254568380 z^6 + 84944630784 z^7 + 71153212416 z^8 + 30922178560 z^9 + 5503713280 z^10) Sin[(5 ArcTan[Sqrt[z]])/4]))/(2284692683845 z^(9/2) (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]