Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7s7)

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=5

http://functions.wolfram.com/07.23.03.a7s7.01

Input Form

Hypergeometric2F1[-(23/4), 5, 19/4, z] == (1/(105671294976 z^(15/4))) (4 z^(3/4) (2590973 + 11743501 z + 63798504 z^2 + 27094537472 z^3 - 178044597350 z^4 + 476947439922 z^5 - 673494597216 z^6 + 530763982056 z^7 - 221793177375 z^8 + 38444150745 z^9) - 100947 (1 - z)^(11/2) (77 + 756 z + 5022 z^2 + 39060 z^3 - 380835 z^4) 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]