Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8954)

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=-23/4, b>=a

For fixed z and a=-23/4, b=-23/4

http://functions.wolfram.com/07.23.03.8954.01

Input Form

Hypergeometric2F1[-(23/4), -(23/4), 13/4, z] == (1/(3940649673949184 z^(9/4))) (9 (8 (1 - z)^(3/4) z^(1/4) (-4043768575 + 203805936180 z + 34603989461664 z^2 + 257105957338496 z^3 + 498006820878336 z^4 + 305608175640576 z^5 + 55588024549376 z^6 + 1989060329472 z^7) - 336490 Sqrt[2] (24035 - 1230592 z + 120598016 z^2 + 1929568256 z^3 + 6891315200 z^4 + 8018984960 z^5 + 3207593984 z^6 + 385875968 z^7 + 8388608 z^8) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 336490 Sqrt[2] (24035 - 1230592 z + 120598016 z^2 + 1929568256 z^3 + 6891315200 z^4 + 8018984960 z^5 + 3207593984 z^6 + 385875968 z^7 + 8388608 z^8) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 168245 Sqrt[2] (24035 - 1230592 z + 120598016 z^2 + 1929568256 z^3 + 6891315200 z^4 + 8018984960 z^5 + 3207593984 z^6 + 385875968 z^7 + 8388608 z^8) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 168245 Sqrt[2] (24035 - 1230592 z + 120598016 z^2 + 1929568256 z^3 + 6891315200 z^4 + 8018984960 z^5 + 3207593984 z^6 + 385875968 z^7 + 8388608 z^8) 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]