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

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=-23/8, b>=a

For fixed z and a=-23/8, b=45/8

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

Input Form

Hypergeometric2F1[-(23/8), 45/8, -(19/4), z] == (1/(93290912 2^(3/4) (-1 + z)^7)) ((1 + Sqrt[1 - z])^(3/4) (-46645456 + 158962804 z - 103571325 z^2 - 86218769 z^3 - 94225495 z^4 + 2342988273 z^5 - 4794541872 z^6 + 4270611840 z^7 - 1842407424 z^8 + 316293120 z^9 + (1/Sqrt[1 - z]) (-46645456 + 182285532 z - 177222045 z^2 - 51388116 z^3 - 46282782 z^4 - 2656715232 z^5 + 8432839939 z^6 - 11181843360 z^7 + 7778352384 z^8 - 2816765952 z^9 + 421724160 z^10)))

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]