Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9345)

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=-5/4

http://functions.wolfram.com/07.23.03.9345.01

Input Form

Hypergeometric2F1[-(23/4), -(5/4), 5/2, -z] == (2 Sqrt[2] (-2 (437 + 17480 z - 230488 z^2 + 268448 z^3 + 8433 z^4 + 1940 z^5 + 330 z^6 + 28 z^7) + (1/Sqrt[1 + z]) (874 + 35397 z - 275369 z^2 - 118498 z^3 + 223416 z^4 + 39473 z^5 + 8743 z^6 + 1404 z^7 + 112 z^8)))/(672945 z^(3/2) Sqrt[-1 + Sqrt[1 + z]])

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]