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

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=-31/8, b>=a

For fixed z and a=-31/8, b=-27/8

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

Input Form

Hypergeometric2F1[-(31/8), -(27/8), 17/4, z] == (1/(9711234785 z^4)) (8 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (4 (-12834 + 271653 z - 3760362 z^2 + 117950877 z^3 + 638582386 z^4 + 679986111 z^5 + 180271962 z^6 + 8857279 z^7) + (1/Sqrt[1 - z]) (51336 - 1112280 z + 15578337 z^2 - 479191614 z^3 - 1713289889 z^4 + 293340964 z^5 + 1538589295 z^6 + 339380178 z^7 + 6653673 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]