Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.an1c)

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=4, b>=a

For fixed z and a=4, b=6

http://functions.wolfram.com/07.23.03.an1c.01

Input Form

Hypergeometric2F1[4, 6, -(23/4), z] == (1/40324038656) (-((1/(-1 + z)^15) (8 (5040504832 - 96646201344 z + 922343178240 z^2 - 5995859279872 z^3 + 31446260514816 z^4 - 159575077552128 z^5 + 1184301927366656 z^6 + 6470526520958835 z^7 + 5179035970060008 z^8 + 895345369664656 z^9 + 10872738100224 z^10 - 187461001728 z^11))) - (1/(1 - z)^(63/4)) (7399583681490 Sqrt[2] z^(27/4) (2821 + 5460 z + 2496 z^2 + 256 z^3) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/(1 - z)^(63/4)) (7399583681490 Sqrt[2] z^(27/4) (2821 + 5460 z + 2496 z^2 + 256 z^3) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/(1 - z)^(63/4)) (3699791840745 Sqrt[2] z^(27/4) (2821 + 5460 z + 2496 z^2 + 256 z^3) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) + (1/(1 - z)^(63/4)) (3699791840745 Sqrt[2] z^(27/4) (2821 + 5460 z + 2496 z^2 + 256 z^3) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))

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]