Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7vr)

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.a7vr.01

Input Form

Hypergeometric2F1[-(23/4), 6, 11/4, z] == (1/(461373440 z^(7/4))) (4 z^(3/4) (33649 + 116780653 z - 1544328123 z^2 + 7289116737 z^3 - 16567100445 z^4 + 19686784887 z^5 - 11807063961 z^6 + 2825809371 z^7) - 100947 (1 - z)^(5/2) (1 + 45 z - 2790 z^2 + 19530 z^3 - 42315 z^4 + 27993 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]