Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7c8)

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=-45/8, b>=a

For fixed z and a=-45/8, b=47/8

http://functions.wolfram.com/07.23.03.b7c8.01

Input Form

Hypergeometric2F1[-(45/8), 47/8, 19/4, z] == (1/(587189905815 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (1982904 + 14240856 z + 106474863 z^2 + 1445298810 z^3 - 29194373769 z^4 + 126363938448 z^5 - 246286213888 z^6 + 248373723136 z^7 - 126902927360 z^8 + 26079133696 z^9 + (1/Sqrt[1 - z]) (4 (-495726 - 3312351 z - 24776643 z^2 - 347539335 z^3 + 16657667289 z^4 - 103038843666 z^5 + 279694909648 z^6 - 407664592896 z^7 + 333480181760 z^8 - 144832331776 z^9 + 26079133696 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]