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

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=-17/8, b>=a

For fixed z and a=-17/8, b=43/8

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

Input Form

Hypergeometric2F1[-(17/8), 43/8, 9/2, -z] == -((256 (Sqrt[z] (-1904 + 7973 z - 35343 z^2 - 1205136 z^3 - 749440 z^4 + 2770944 z^5 + 2342912 z^6) Cos[(7 ArcTan[Sqrt[z]])/4] - (-1088 + 5304 z - 23375 z^2 + 203949 z^3 + 3784032 z^4 + 7667968 z^5 + 4100096 z^6) Sin[(7 ArcTan[Sqrt[z]])/4]))/ (393571035 z^(7/2) (1 + z)^(7/8)))

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]