Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8yq)

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=-21/4, b>=a

For fixed z and a=-21/4, b=23/4

http://functions.wolfram.com/07.23.03.a8yq.01

Input Form

Hypergeometric2F1[-(21/4), 23/4, 2, z] == -((1/(72747675 Pi z)) (8 (2 (153153 - 35107087 z + 425478560 z^2 - 1733847040 z^3 + 3129999360 z^4 - 2592079872 z^5 + 805306368 z^6) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (-153153 (1 + Sqrt[1 - z]) + (35107087 + 16881880 Sqrt[1 - z]) z - 160 (2659241 + 938608 Sqrt[1 - z]) z^2 + 10240 (169321 + 42528 Sqrt[1 - z]) z^3 - 15728640 (199 + 32 Sqrt[1 - z]) z^4 + 25165824 (103 + 8 Sqrt[1 - z]) z^5 - 805306368 z^6) 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]