Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8033)

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=4/3, b>=a

For fixed z and a=4/3, b=17/3

http://functions.wolfram.com/07.23.03.8033.01

Input Form

Hypergeometric2F1[4/3, 17/3, -(9/2), -z] == ((13436928 + 177831936 z + 1130434560 z^2 + 4737671168 z^3 + 16074471424 z^4 + 72405983232 z^5 - 124001665031 z^6 - 3991781560 z^7 - 735583608 z^8 - 102685984 z^9 - 7256960 z^10) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (4478976 + 56125440 z + 337659904 z^2 + 1345755136 z^3 + 4435087360 z^4 - 53810647061 z^5 + 3660229200 z^6 + 686961976 z^7 + 99057504 z^8 + 7256960 z^9) Sinh[ArcSinh[Sqrt[z]]/3])/ (13436928 (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]