Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5m3)

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=-47/8, b>=a

For fixed z and a=-47/8, b=37/8

http://functions.wolfram.com/07.23.03.b5m3.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, 1/4, z] == (1/(101065 2^(3/4))) ((1 + Sqrt[1 - z])^(3/4) (4 (-1658728 + 25251701 z - 115830336 z^2 + 225362176 z^3 - 196640768 z^4 + 63504384 z^5) + (1/Sqrt[1 - z]) (6735977 - 115340345 z + 636901072 z^2 - 1615358720 z^3 + 2086420480 z^4 - 1338048512 z^5 + 338690048 z^6)))

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]