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

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=4

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

Input Form

Hypergeometric2F1[-(11/4), 4, -(21/4), z] == (1/(891072 (-1 + z)^7)) (4 (-222768 + 1092624 z - 1891344 z^2 + 1136688 z^3 + 44800 z^4 + 130816 z^5 + 1507072 z^6 - 5336863 z^7 + 5806625 z^8 - 2772385 z^9 + 504735 z^10) - 231 Sqrt[1 - z] z^(25/4) (-11803 + 18315 z - 10545 z^2 + 2185 z^3) 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]