Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bpi9)

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=47/8

http://functions.wolfram.com/07.23.03.bpi9.01

Input Form

Hypergeometric2F1[-(15/8), 47/8, 11/2, -z] == (1/(4248325653 z^(9/2) Sqrt[1 + z])) (1024 (4 Sqrt[z] Sqrt[1 + z] (560 - 1490 z + 3839 z^2 - 12430 z^3 + 1126092 z^4 + 2538096 z^5 + 1384416 z^6) Cosh[ArcSinh[Sqrt[z]]/4] - (8960 - 17680 z + 44299 z^2 - 154341 z^3 + 1279520 z^4 + 8888352 z^5 + 12921216 z^6 + 5537664 z^7) 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]