Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c7nk)

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=19/8, b>=a

For fixed z and a=19/8, b=47/8

http://functions.wolfram.com/07.23.03.c7nk.01

Input Form

Hypergeometric2F1[19/8, 47/8, -(11/2), -z] == (1/(45056 (1 + z)^(107/8))) ((45056 + 704256 z + 5359648 z^2 + 27081131 z^3 + 107459022 z^4 + 407416009 z^5 + 2645134492 z^6 - 4888700019 z^7 + 853367438 z^8 + 46862431 z^9 + 3561096 z^10 + 165440 z^11) Cos[(3 ArcTan[Sqrt[z]])/4] + Sqrt[z] (33792 + 523264 z + 3944556 z^2 + 19752557 z^3 + 77837606 z^4 + 294813519 z^5 - 4919803952 z^6 + 2836084699 z^7 - 34764114 z^8 - 2652727 z^9 - 124080 z^10) Sin[(3 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]