Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bm5i)

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=-21/8, b>=a

For fixed z and a=-21/8, b=45/8

http://functions.wolfram.com/07.23.03.bm5i.01

Input Form

Hypergeometric2F1[-(21/8), 45/8, -(1/2), z] == -((1/(4292 (1 - z)^(7/2))) (Sqrt[1 - z] (-4292 - 112665 z + 2204517 z^2 - 9092552 z^3 + 15191472 z^4 - 11342400 z^5 + 3155200 z^6) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (-3219 - 671034 z + 5437509 z^2 - 15467688 z^3 + 20468272 z^4 - 12920000 z^5 + 3155200 z^6) Sin[(3 ArcSin[Sqrt[z]])/4]))

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]