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

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=-35/8, b>=a

For fixed z and a=-35/8, b=17/8

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

Input Form

Hypergeometric2F1[-(35/8), 17/8, 5/2, z] == (1/(435643 z^(3/2))) (8 ((1 + Sqrt[z])^(19/4) (-2508 + 11913 Sqrt[z] - 52668 z + 191776 z^(3/2) - 384256 z^2 + 404736 z^(5/2) - 214016 z^3 + 45056 z^(7/2)) + (1 - Sqrt[z])^(19/4) (2508 + 11913 Sqrt[z] + 52668 z + 191776 z^(3/2) + 384256 z^2 + 404736 z^(5/2) + 214016 z^3 + 45056 z^(7/2))))

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]