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

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=-19/8, b>=a

For fixed z and a=-19/8, b=-15/8

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

Input Form

Hypergeometric2F1[-(19/8), -(15/8), 21/4, z] == (16 2^(1/4) (4 (494 - 6137 z + 39140 z^2 - 198702 z^3 + 6728442 z^4 + 7031631 z^5 + 888588 z^6) + (1/Sqrt[1 - z]) (-1976 + 25536 z - 168587 z^2 + 870143 z^3 + 8410010 z^4 - 4559234 z^5 - 4405127 z^6 - 170765 z^7)))/(571249105 (1 + Sqrt[1 - z])^(1/4) z^4)

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]