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

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=-39/8, b>=a

For fixed z and a=-39/8, b=19/8

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

Input Form

Hypergeometric2F1[-(39/8), 19/8, 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-2190336 + 9331744 z - 8110375 z^2 - 14598675 z^3 + 76918355 z^4 - 115483457 z^5 + 86757528 z^6 - 33468240 z^7 + 5304000 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-2190336 + 9331744 z - 8110375 z^2 - 14598675 z^3 + 76918355 z^4 - 115483457 z^5 + 86757528 z^6 - 33468240 z^7 + 5304000 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-2190336 + 9331744 z - 8110375 z^2 - 14598675 z^3 + 76918355 z^4 - 115483457 z^5 + 86757528 z^6 - 33468240 z^7 + 5304000 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 8 (-273792 + 1337588 z - 1714765 z^2 - 1297660 z^3 - 11674940 z^4 + 32886106 z^5 - 39851279 z^6 + 26128830 z^7 - 9096360 z^8 + 1326000 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (5894609195475 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]