Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bcj0)

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=-17/8

http://functions.wolfram.com/07.23.03.bcj0.01

Input Form

Hypergeometric2F1[-(35/8), -(17/8), 6, z] == (1/(12284725198890375 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-294912 + 4910976 z - 41878971 z^2 + 263348892 z^3 - 1732003425 z^4 - 66950144430 z^5 - 87466854685 z^6 - 19627449240 z^7 - 23931495 z^8 + 731850 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 6 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (18432 - 293544 z + 2405457 z^2 - 14731650 z^3 - 7712711325 z^4 - 11386763220 z^5 - 2823129785 z^6 - 11855970 z^7 + 365925 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (36864 - 607824 z + 5136993 z^2 - 32105250 z^3 + 9583976295 z^4 + 17798891160 z^5 + 7217010815 z^6 + 551961270 z^7 - 9879975 z^8 + 292740 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-294912 + 4910976 z - 41878971 z^2 + 263348892 z^3 - 1732003425 z^4 - 66950144430 z^5 - 87466854685 z^6 - 19627449240 z^7 - 23931495 z^8 + 731850 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]