Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab8z)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-15/4, b>=a

For fixed z and a=-15/4, b=-3/4

http://functions.wolfram.com/07.23.03.ab8z.01

Input Form

Hypergeometric2F1[-(15/4), -(3/4), 6, z] == (1/(430771637835 Pi z^5)) (16384 (2 Sqrt[1 - z] (6144 - 73824 z + 433321 z^2 - 1764651 z^3 + 6960450 z^4 + 24572674 z^5 + 2321781 z^6 - 221559 z^7 + 13984 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (6144 - 78432 z + 488257 z^2 - 2084649 z^3 + 8255730 z^4 - 33120626 z^5 - 37910187 z^6 - 56373 z^7 + 3496 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (6144 - 73824 z + 433321 z^2 - 1764651 z^3 + 6960450 z^4 + 24572674 z^5 + 2321781 z^6 - 221559 z^7 + 13984 z^8) EllipticK[(1/2) (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]