Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9jp)

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=25/8, b>=a

For fixed z and a=25/8, b=29/8

http://functions.wolfram.com/07.23.03.c9jp.01

Input Form

Hypergeometric2F1[25/8, 29/8, -(23/4), z] == (1/(27968 2^(3/4) (-1 + z)^12)) ((1 + Sqrt[1 - z])^(3/4) (-2 (-6992 + 96368 z - 636735 z^2 + 2735742 z^3 - 8947605 z^4 + 26333316 z^5 + 1613013831 z^6 + 1028622510 z^7 + 88155837 z^8) + (1/Sqrt[1 - z]) (13984 - 199728 z + 1368090 z^2 - 6085001 z^3 + 20483268 z^4 - 61002747 z^5 + 3667044714 z^6 + 3217325985 z^7 + 485556984 z^8 + 7137843 z^9)))

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]