Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9xd)

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=-19/4, b>=a

For fixed z and a=-19/4, b=6

http://functions.wolfram.com/07.23.03.a9xd.01

Input Form

Hypergeometric2F1[-(19/4), 6, -(13/4), z] == (1/(2555904 (-1 + z)^5)) (4 (-1 + z) (638976 + 3047424 z + 14106624 z^2 + 92078080 z^3 + 2427502592 z^4 - 18908871573 z^5 + 48600254052 z^6 - 58450130046 z^7 + 33909712452 z^8 - 7688830149 z^9) + 4389 Sqrt[1 - z] z^(17/4) (-1239315 + 6786725 z - 14659326 z^2 + 15670314 z^3 - 8310015 z^4 + 1751841 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]