Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b802)

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=-43/8, b>=a

For fixed z and a=-43/8, b=25/8

http://functions.wolfram.com/07.23.03.b802.01

Input Form

Hypergeometric2F1[-(43/8), 25/8, -(9/2), -z] == (1/(156672 (1 + z)^(13/8))) ((156672 - 452608 z + 992460 z^2 - 2121855 z^3 + 5279520 z^4 - 25420032 z^5 + 106016768 z^6 + 140574720 z^7) Cos[(5 ArcTan[Sqrt[z]])/4] + Sqrt[z] (195840 - 529040 z + 1135413 z^2 - 2421072 z^3 + 6103680 z^4 - 165468160 z^5 - 175718400 z^6) Sin[(5 ArcTan[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]