Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7vf)

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=-23/4, b>=a

For fixed z and a=-23/4, b=6

http://functions.wolfram.com/07.23.03.a7vf.01

Input Form

Hypergeometric2F1[-(23/4), 6, -(9/4), z] == (1/(3932160 (-1 + z)^3)) (4 (-1 + z) (983040 + 13107200 z + 171311104 z^2 + 7633108992 z^3 - 88380869661 z^4 + 318801821940 z^5 - 514184648670 z^6 + 386150136372 z^7 - 110206565469 z^8) + 100947 Sqrt[1 - z] z^(13/4) (-189805 + 1507275 z - 4450050 z^2 + 6230070 z^3 - 4189185 z^4 + 1091727 z^5) Beta[z, 3/4, 1/2])

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]