Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5ia)

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=-47/8, b>=a

For fixed z and a=-47/8, b=31/8

http://functions.wolfram.com/07.23.03.b5ia.01

Input Form

Hypergeometric2F1[-(47/8), 31/8, -(9/2), -z] == (1/(322560 (1 + z)^(5/2))) (-2 Sqrt[1 + z] (-161280 + 488320 z - 1282490 z^2 + 3637601 z^3 - 13521255 z^4 + 116137120 z^5 + 822012048 z^6 + 1209136896 z^7 + 522466560 z^8) Cosh[ArcSinh[Sqrt[z]]/4] + Sqrt[z] (-80640 + 218960 z - 554235 z^2 + 1579743 z^3 - 6083990 z^4 + 817310384 z^5 + 2722544352 z^6 + 2940740352 z^7 + 1044933120 z^8) Sinh[ArcSinh[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]