Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8298)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=7/3, b>=a

For fixed z and a=7/3, b=11/3

http://functions.wolfram.com/07.23.03.8298.01

Input Form

Hypergeometric2F1[7/3, 11/3, -(11/2), -z] == ((40310784 + 528519168 z + 3291770880 z^2 + 13164806144 z^3 + 39393011712 z^4 + 104208715776 z^5 + 407514652672 z^6 - 788289260325 z^7 + 144994909116 z^8 + 349604048 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-13436928 - 166717440 z - 980969472 z^2 - 3710261248 z^3 - 10589511680 z^4 - 27536330752 z^5 + 307625709935 z^6 - 93952718108 z^7 + 349604048 z^8) Sinh[ArcSinh[Sqrt[z]]/3])/(40310784 (1 + z)^(23/2))

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]