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

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=-1/8

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

Input Form

Hypergeometric2F1[-(15/8), -(1/8), 11/2, z] == (1/(6393342813 z^(9/2))) (1024 (-2 Sqrt[z] (-1120 + 9260 z - 35371 z^2 + 88700 z^3 - 3366602 z^4 - 223184 z^5 + 13949 z^6) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) ((8960 - 80240 z + 333163 z^2 - 898418 z^3 + 2426170 z^4 - 1357216 z^5 - 460317 z^6 + 27898 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]