Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b526)

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=-47/8, b>=a

For fixed z and a=-47/8, b=3/8

http://functions.wolfram.com/07.23.03.b526.01

Input Form

Hypergeometric2F1[-(47/8), 3/8, 5, z] == (65536 2^(1/4) (-4 Sqrt[1 - z] (51472896 - 586040368 z + 3262731493 z^2 - 13540488171 z^3 - 16463440070 z^4 + 9741851042 z^5 - 4731393471 z^6 + 1613723241 z^7 - 337164672 z^8 + 32301360 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (51472896 - 586040368 z + 3262731493 z^2 - 13540488171 z^3 - 16463440070 z^4 + 9741851042 z^5 - 4731393471 z^6 + 1613723241 z^7 - 337164672 z^8 + 32301360 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 Sqrt[1 - z] (51472896 - 586040368 z + 3262731493 z^2 - 13540488171 z^3 - 16463440070 z^4 + 9741851042 z^5 - 4731393471 z^6 + 1613723241 z^7 - 337164672 z^8 + 32301360 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (102945792 - 1236421856 z + 7247457481 z^2 - 31044154757 z^3 + 245645036210 z^4 - 85294360186 z^5 + 48658740893 z^6 - 22317981153 z^7 + 7180827576 z^8 - 1419721680 z^9 + 129205440 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (8593804333439325 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^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]