Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.am6y)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=3, b>=a

For fixed z and a=3, b=6

http://functions.wolfram.com/07.23.03.am6y.01

Input Form

Hypergeometric2F1[3, 6, -(17/4), z] == (1/1390411776) ((1/(-1 + z)^13) (8 (-173801472 + 2995519488 z - 26296713216 z^2 + 167135150080 z^3 - 1029335941120 z^4 + 17125194596352 z^5 + 41643190273877 z^6 + 16094420767636 z^7 + 322367572800 z^8 - 17485802880 z^9 + 689095680 z^10)) + (336882996450 Sqrt[2] z^(21/4) (145 + 232 z + 64 z^2) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(53/4) + (336882996450 Sqrt[2] z^(21/4) (145 + 232 z + 64 z^2) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(53/4) - (168441498225 Sqrt[2] z^(21/4) (145 + 232 z + 64 z^2) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(53/4) + (168441498225 Sqrt[2] z^(21/4) (145 + 232 z + 64 z^2) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(53/4))

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]