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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-39/8, b>=a

For fixed z and a=-39/8, b=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, 21/4, z] == (1/(164444294245 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (1334736 + 4902588 z + 21059881 z^2 + 137242518 z^3 + 3769044201 z^4 - 26042334516 z^5 + 61939924992 z^6 - 70091265024 z^7 + 38640746496 z^8 - 8382578688 z^9 - (1/Sqrt[1 - z]) (1334736 + 4235220 z + 18441745 z^2 + 126016333 z^3 + 3697431907 z^4 - 33084440373 z^5 + 102927794640 z^6 - 160888772352 z^7 + 137089007616 z^8 - 61067821056 z^9 + 11176771584 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]