Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc98)

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=-37/8, b>=a

For fixed z and a=-37/8, b=41/8

http://functions.wolfram.com/07.23.03.bc98.01

Input Form

Hypergeometric2F1[-(37/8), 41/8, 5, z] == (65536 2^(1/4) (4 Sqrt[1 - z] (-49993216 - 189036848 z - 764251761 z^2 - 4963193690 z^3 + 283694603195 z^4 - 1062599669904 z^5 + 1551529547568 z^6 - 1019018778624 z^7 + 252351348480 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-49993216 - 189036848 z - 764251761 z^2 - 4963193690 z^3 + 283694603195 z^4 - 1062599669904 z^5 + 1551529547568 z^6 - 1019018778624 z^7 + 252351348480 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-99986432 - 315582176 z - 1281954947 z^2 - 8927499490 z^3 + 154242633005 z^4 - 470221030168 z^5 + 607269484656 z^6 - 364707782208 z^7 + 84117116160 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 Sqrt[1 - z] (-49993216 - 189036848 z - 764251761 z^2 - 4963193690 z^3 + 283694603195 z^4 - 1062599669904 z^5 + 1551529547568 z^6 - 1019018778624 z^7 + 252351348480 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (13747106377879875 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]