Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.by1k)

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=1/8, b>=a

For fixed z and a=1/8, b=39/8

http://functions.wolfram.com/07.23.03.by1k.01

Input Form

Hypergeometric2F1[1/8, 39/8, -(9/2), z] == -((1/(15332352 (1 - z)^(19/2))) (Sqrt[1 - z] (-15332352 + 140546560 z - 576831260 z^2 + 1400666397 z^3 - 2264978544 z^4 + 2924017278 z^5 - 1649887720 z^6 + 661531325 z^7 - 158962804 z^8 + 17185168 z^9) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (-3833088 + 36334480 z - 154678933 z^2 + 390861609 z^3 - 659038734 z^4 + 3675533602 z^5 - 1961857105 z^6 + 738864581 z^7 - 167555388 z^8 + 17185168 z^9) 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]