Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bp9q)

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=-15/8, b>=a

For fixed z and a=-15/8, b=37/8

http://functions.wolfram.com/07.23.03.bp9q.01

Input Form

Hypergeometric2F1[-(15/8), 37/8, -(11/4), z] == (1/(33176 2^(3/4) (-1 + z)^5)) ((1 + Sqrt[1 - z])^(3/4) (-16588 + 27521 z + 26390 z^2 - 417327 z^3 + 678756 z^4 - 434688 z^5 + 101376 z^6 + (1/Sqrt[1 - z]) (-16588 + 35815 z + 14703 z^2 + 488957 z^3 - 1312487 z^4 + 1395552 z^5 - 695040 z^6 + 135168 z^7)))

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]