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

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=21/4

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

Input Form

Hypergeometric2F1[19/4, 21/4, -(11/2), -z] == (1/(2112 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z] ((1/(1 + z)^15) (1056 + 20496 z + 199298 z^2 + 1334975 z^3 + 7374289 z^4 + 41582827 z^5 - 2564914423 z^6 + 4564298845 z^7 - 1971591965 z^8 + 204960937 z^9 - 2419615 z^10) + (1/(1 + z)^(31/2)) (2 (528 + 10512 z + 104707 z^2 + 716064 z^3 + 4009052 z^4 + 22557392 z^5 + 1730661754 z^6 - 4367763328 z^7 + 2756813852 z^8 - 489836544 z^9 + 17643643 z^10))))

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]