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

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=47/8

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

Input Form

Hypergeometric2F1[43/8, 47/8, -(11/2), -z] == (1/(135168 (1 + z)^(131/8))) ((135168 + 2951424 z + 32688992 z^2 + 253170005 z^3 + 1646727912 z^4 + 11178734476 z^5 + 145521592216 z^6 - 817256888706 z^7 + 915045865048 z^8 - 298408345844 z^9 + 25222737480 z^10 - 252287211 z^11) Cos[(3 ArcTan[Sqrt[z]])/4] + 4 Sqrt[z] (25344 + 549696 z + 6049869 z^2 + 46605076 z^3 + 302158696 z^4 + 2053415364 z^5 - 112896988118 z^6 + 253825284412 z^7 - 152286051456 z^8 + 26260395308 z^9 - 927047647 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]