Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bp19)

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=-15/8, b>=a

For fixed z and a=-15/8, b=23/8

http://functions.wolfram.com/07.23.03.bp19.01

Input Form

Hypergeometric2F1[-(15/8), 23/8, 11/2, z] == (1/(5958381 z^(9/2))) (1024 (Sqrt[z] (448 - 1256 z + 715 z^2 + 390 z^3 + 6643 z^4 - 7436 z^5 + 2288 z^6) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-1792 + 6256 z - 6167 z^2 + 65 z^3 - 2145 z^4 + 10075 z^5 - 8580 z^6 + 2288 z^7) 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]