Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bdd7)

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=47/8

http://functions.wolfram.com/07.23.03.bdd7.01

Input Form

Hypergeometric2F1[-(35/8), 47/8, 6, z] == (1/(79349907922310025 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-61636608 - 129292416 z - 337863339 z^2 - 1187497872 z^3 - 7282432575 z^4 + 171557122890 z^5 - 545381823920 z^6 + 715616634720 z^7 - 432875139840 z^8 + 100164979200 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 6 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (3852288 + 10879704 z + 29292813 z^2 + 96401250 z^3 + 50977028025 z^4 - 203588462640 z^5 + 303811723280 z^6 - 201412823040 z^7 + 50082489600 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (7704576 + 17425584 z + 45476937 z^2 + 156969450 z^3 - 59600265615 z^4 + 271167164220 z^5 - 499803858320 z^6 + 463146128640 z^7 - 215219347200 z^8 + 40065991680 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-61636608 - 129292416 z - 337863339 z^2 - 1187497872 z^3 - 7282432575 z^4 + 171557122890 z^5 - 545381823920 z^6 + 715616634720 z^7 - 432875139840 z^8 + 100164979200 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]