Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9yx)

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=25/8, b>=a

For fixed z and a=25/8, b=47/8

http://functions.wolfram.com/07.23.03.c9yx.01

Input Form

Hypergeometric2F1[25/8, 47/8, -(11/2), z] == (1/(4190208 (1 - z)^(29/2))) (Sqrt[1 - z] (4190208 - 72781056 z + 623431328 z^2 - 3603211313 z^3 + 16695173287 z^4 - 75866047257 z^5 + 607776367835 z^6 + 1797480461313 z^7 + 779225304261 z^8 + 34790691261 z^9 - 1300878375 z^10 + 41628108 z^11) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (1047552 - 18522624 z + 161404724 z^2 - 947172915 z^3 + 4435947945 z^4 - 20162338651 z^5 + 4414085625557 z^6 + 6416723086443 z^7 + 1774742377755 z^8 + 35435926935 z^9 - 1321692429 z^10 + 41628108 z^11) Sin[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]