Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7vj)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=6

http://functions.wolfram.com/07.23.03.a7vj.01

Input Form

Hypergeometric2F1[-(23/4), 6, -(1/4), z] == (1/1048576) (4 (262144 + 36175872 z - 839080641 z^2 + 5113450620 z^3 - 12593426670 z^4 + 13506304812 z^5 - 5247931689 z^6) - (1/Sqrt[1 - z]) (100947 z^(5/4) (-1105 + 16575 z - 79050 z^2 + 162750 z^3 - 151125 z^4 + 51987 z^5) Beta[z, 3/4, 1/2]))

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]