Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9qv)

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=-39/8, b>=a

For fixed z and a=-39/8, b=-27/8

http://functions.wolfram.com/07.23.03.b9qv.01

Input Form

Hypergeometric2F1[-(39/8), -(27/8), 13/4, z] == (1/(183230845 z^3)) (4 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (8556 - 275931 z + 15593310 z^2 + 136884091 z^3 + 233761728 z^4 + 103559211 z^5 + 9620182 z^6 - 28971 z^7 + (1/Sqrt[1 - z]) (-8556 + 280209 z - 15730206 z^2 - 106217537 z^3 - 54594116 z^4 + 117706687 z^5 + 55888530 z^6 + 2713617 z^7 - 38628 z^8)))

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]