Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7x3)

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=-43/8, b>=a

For fixed z and a=-43/8, b=17/8

http://functions.wolfram.com/07.23.03.b7x3.01

Input Form

Hypergeometric2F1[-(43/8), 17/8, 5, z] == (65536 2^(1/4) (-16 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (3451008 - 19088388 z + 31139955 z^2 + 19816335 z^3 - 222502845 z^4 + 427963917 z^5 - 426299342 z^6 + 244159440 z^7 - 76581120 z^8 + 10250240 z^9) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 8 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (3451008 - 19088388 z + 31139955 z^2 + 19816335 z^3 - 222502845 z^4 + 427963917 z^5 - 426299342 z^6 + 244159440 z^7 - 76581120 z^8 + 10250240 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 8 Sqrt[1 - z] (3451008 - 19088388 z + 31139955 z^2 + 19816335 z^3 - 222502845 z^4 + 427963917 z^5 - 426299342 z^6 + 244159440 z^7 - 76581120 z^8 + 10250240 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (27608064 - 163060128 z + 303553899 z^2 + 79265340 z^3 - 551409990 z^4 + 980055276 z^5 - 931665037 z^6 + 515210976 z^7 - 157006080 z^8 + 20500480 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(42803920553625 Pi (1 + Sqrt[1 - z])^(1/4) 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]