Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bd3o)

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=-35/8, b>=a

For fixed z and a=-35/8, b=31/8

http://functions.wolfram.com/07.23.03.bd3o.01

Input Form

Hypergeometric2F1[-(35/8), 31/8, 6, z] == (1/(196898034546675 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-20545536 + 53209728 z - 7285113 z^2 - 9835749 z^3 - 30613275 z^4 + 381674505 z^5 - 801541840 z^6 + 750834240 z^7 - 341153280 z^8 + 61526400 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (642048 - 1196316 z - 596277 z^2 - 188100 z^3 + 63342675 z^4 - 159925290 z^5 + 165480380 z^6 - 80673840 z^7 + 15381600 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (2568192 - 6229872 z + 16929 z^2 + 987525 z^3 - 146351205 z^4 + 459508215 z^5 - 620665240 z^6 + 440603280 z^7 - 162302400 z^8 + 24610560 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-20545536 + 53209728 z - 7285113 z^2 - 9835749 z^3 - 30613275 z^4 + 381674505 z^5 - 801541840 z^6 + 750834240 z^7 - 341153280 z^8 + 61526400 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + 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]