Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.adr7)

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=-11/4, b>=a

For fixed z and a=-11/4, b=6

http://functions.wolfram.com/07.23.03.adr7.01

Input Form

Hypergeometric2F1[-(11/4), 6, -(17/4), z] == (1/(27156480 (-1 + z)^8)) (4 (6789120 - 27955200 z + 28907520 z^2 + 4587520 z^3 + 16973824 z^4 + 277086208 z^5 - 1520819923 z^6 + 3017727011 z^7 - 3168532150 z^8 + 1895813502 z^9 - 615070071 z^10 + 84492639 z^11) - 231 Sqrt[1 - z] z^(21/4) (-2419615 + 7258845 z - 9511590 z^2 + 6629290 z^3 - 2418795 z^4 + 365769 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]