Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ali1)

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=9/4, b>=a

For fixed z and a=9/4, b=6

http://functions.wolfram.com/07.23.03.ali1.01

Input Form

Hypergeometric2F1[9/4, 6, -(9/4), z] == (1/(5120 (-1 + z)^11)) (4 (-1280 + 21760 z - 224768 z^2 + 4570624 z^3 + 5529871 z^4 - 8282987 z^5 - 1806490 z^6 + 216986 z^7 - 25333 z^8 + 1617 z^9) - 231 Sqrt[1 - z] z^(13/4) (-51765 - 76125 z - 7250 z^2 + 870 z^3 - 105 z^4 + 7 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]