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

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=-11/4, b>=a

For fixed z and a=-11/4, b=15/4

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

Input Form

Hypergeometric2F1[-(11/4), 15/4, -(7/2), -z] == (Sqrt[z] ((56 + 52 z - 54 z^2 + 76 z^3 + 758 z^4 + 864 z^5 + 288 z^6)/ (1 + z)^4 + (56 + 80 z - 35 z^2 + 46 z^3 - 1199 z^4 - 2776 z^5 - 2160 z^6 - 576 z^7)/(1 + z)^(9/2)))/(112 Sqrt[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]