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

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=-23/8, b>=a

For fixed z and a=-23/8, b=-3/8

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

Input Form

Hypergeometric2F1[-(23/8), -(3/8), 21/4, z] == (1/(2252661565 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (71760 - 741060 z + 3722665 z^2 - 13515904 z^3 + 88574886 z^4 + 64568672 z^5 - 2273687 z^6 + 167388 z^7 + (1/Sqrt[1 - z]) (-71760 + 776940 z - 4084225 z^2 + 15289089 z^3 - 94911018 z^4 + 48630638 z^5 + 37369371 z^6 - 3222219 z^7 + 223184 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]