Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bd8b)

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=39/8

http://functions.wolfram.com/07.23.03.bd8b.01

Input Form

Hypergeometric2F1[-(35/8), 39/8, 6, z] == (1/(2034613023648975 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (61636608 - 15168384 z - 21783861 z^2 - 51563853 z^3 - 235454175 z^4 + 4197340585 z^5 - 11059745080 z^6 + 12424991280 z^7 - 6577172160 z^8 + 1353580800 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-7704576 - 3701808 z - 509751 z^2 + 5548950 z^3 + 2620280025 z^4 - 8524601720 z^5 + 10747371440 z^6 - 6171097920 z^7 + 1353580800 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-3852288 + 316008 z + 1220769 z^2 + 3338775 z^3 - 760873905 z^4 + 2923730465 z^5 - 4675617440 z^6 + 3833041680 z^7 - 1599686400 z^8 + 270716160 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (61636608 - 15168384 z - 21783861 z^2 - 51563853 z^3 - 235454175 z^4 + 4197340585 z^5 - 11059745080 z^6 + 12424991280 z^7 - 6577172160 z^8 + 1353580800 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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</apply> </annotation-xml> </semantics> </math>

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]