Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.acl7)

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=-13/4, b>=a

For fixed z and a=-13/4, b=9/4

http://functions.wolfram.com/07.23.03.acl7.01

Input Form

Hypergeometric2F1[-(13/4), 9/4, 11/2, -z] == (16 Sqrt[2] (-1456 - 7436 z - 13091 z^2 - 5187 z^3 + 6825 z^4 + 26123 z^5 + 25814 z^6 + 11536 z^7 + 2016 z^8 + (1/Sqrt[1 + z]) (1456 + 8164 z + 16627 z^2 + 10894 z^3 - 5460 z^4 - 15646 z^5 - 14223 z^6 - 6020 z^7 - 1008 z^8)))/(447051 z^(9/2) 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]