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

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=-31/8, b>=a

For fixed z and a=-31/8, b=-25/8

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

Input Form

Hypergeometric2F1[-(31/8), -(25/8), 11/2, -z] == (1024 (Sqrt[z] Sqrt[1 + z] (7985600 + 144453800 z + 1401569055 z^2 + 11133102850 z^3 + 4833004718769 z^4 - 11103293561308 z^5 + 5515279981137 z^6 - 571832563182 z^7 + 3382283775 z^8) Cosh[ArcSinh[Sqrt[z]]/4] - (31942400 + 599775600 z + 6000903895 z^2 + 48340590745 z^3 + 587556829875 z^4 - 2110502991539 z^5 - 623655797947 z^6 + 1723935285099 z^7 - 304178934543 z^8 + 3382283775 z^9) Sinh[ArcSinh[Sqrt[z]]/4]))/ (4806307907290461 z^(9/2) Sqrt[1 + z])

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]