Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c3u4)

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=11/8, b>=a

For fixed z and a=11/8, b=45/8

http://functions.wolfram.com/07.23.03.c3u4.01

Input Form

Hypergeometric2F1[11/8, 45/8, -(11/2), -z] == (1/(30765056 (1 + z)^(25/2))) ((-Sqrt[1 + z]) (-30765056 - 421096704 z - 2738811040 z^2 - 11423107569 z^3 - 35481459690 z^4 - 96296581359 z^5 - 376389849976 z^6 + 371477980305 z^7 + 27458712334 z^8 + 4335820735 z^9 + 540867540 z^10 + 34851440 z^11) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-23073792 - 319187456 z - 2098062652 z^2 - 8839602549 z^3 - 27692659990 z^4 - 75441096683 z^5 - 568036588404 z^6 + 384697801717 z^7 + 29561192474 z^8 + 4601898075 z^9 + 558293260 z^10 + 34851440 z^11) Sinh[(3 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]