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

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=21/4

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

Input Form

Hypergeometric2F1[-(15/4), 21/4, 5, z] == (1/(93364366095 Pi z^4)) (4096 (-2 Sqrt[1 - z] (29568 + 112112 z + 428967 z^2 + 2513973 z^3 - 69637504 z^4 + 188135424 z^5 - 180289536 z^6 + 58720256 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] + 4 (7392 + 22484 z + 85701 z^2 + 545853 z^3 - 6492316 z^4 + 14454528 z^5 - 12300288 z^6 + 3670016 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (29568 + 112112 z + 428967 z^2 + 2513973 z^3 - 69637504 z^4 + 188135424 z^5 - 180289536 z^6 + 58720256 z^7) 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]