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

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=-33/8

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

Input Form

Hypergeometric2F1[-(35/8), -(33/8), 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (3244032 - 69227136 z + 783646281 z^2 - 6855335487 z^3 + 66958508925 z^4 + 4442293034821 z^5 + 11585623950587 z^6 + 7732632060483 z^7 + 1412775932799 z^8 + 48447608055 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-101376 + 2089692 z - 22977801 z^2 + 197678250 z^3 + 245119176225 z^4 + 714866743672 z^5 + 515437180841 z^6 + 100843323042 z^7 + 3718976415 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (405504 - 8586864 z + 96567273 z^2 - 841492575 z^3 + 601203296925 z^4 + 2015852768837 z^5 + 1838493839323 z^6 + 551501153379 z^7 + 49456754655 z^8 + 763978215 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (3244032 - 69227136 z + 783646281 z^2 - 6855335487 z^3 + 66958508925 z^4 + 4442293034821 z^5 + 11585623950587 z^6 + 7732632060483 z^7 + 1412775932799 z^8 + 48447608055 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (777213614249797725 Pi z^5)

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]