Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bvx4)

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=-3/8, b>=a

For fixed z and a=-3/8, b=33/8

http://functions.wolfram.com/07.23.03.bvx4.01

Input Form

Hypergeometric2F1[-(3/8), 33/8, -(15/4), z] == (-6800 + 45220 z - 124185 z^2 + 171275 z^3 - 72675 z^4 + 60021 z^5 - 23256 z^6 + 3648 z^7 + (1/Sqrt[1 - z]) (-6800 + 48620 z - 145945 z^2 + 228140 z^3 - 145350 z^4 + 448704 z^5 - 302841 z^6 + 103056 z^7 - 14592 z^8))/(6800 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + 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]